references - springer978-3-642-61586-3/1.pdf · 264 references e.j. davison (1977): connectability...

References

A.V. Aho, J.E. Hopcroft and J.D. Ullman (1974): The Design and

Analysis of Computer Algorithms. Addison-Wesley, Reading,

Massachusetts.

M. Aigner (1979): Combinatorial Theory. Springer, Ber~in.

B.D.O. Anderson and D.J. Clements (1981): Algebraic characterization

of fixed modes in decentralized control. Automatica, 11, 703-712.

B.D.O. Anderson and H.-M. Hong (1982): Structural controllability and

matrix nets. Int. ~ Control, ]2, 397-416.

W.N. Anderson, Jr. (1975): Maximum matching and the rank of a matrix.

SIAM ~ AP.P1..:. Math., 28, 114-123.

T. Aoki, S. Hosoe and Y. Hayakawa (1983): Structural controllability

for linear systems in descriptor form (in Japanese). Trans. Soc.

Instr. Control Engin., 12, 628-635.

O. Aono (1982): Dimensions and Dimensional Analysis (Jigen to

Jigen-Kaiseki, in Japanese). Kyoritsu Shuppan, Tokyo.

A. Baker (1975): Transcendental Number Theory. Cambridge Univ. Press.

F.L. Bauer (1974): Computational graphs and rounding error. SIAM ~

Numer. Anal., 11, 87-96.

W. Bauer and V. Strassen (1983): The complexity of partial derivatives.

Theor. Comput. Sci., 22, 317-330.

G. Birkhoff (1967): Lattice Theory (3rd ed.). Amer. Math. Soc. Colloq.

Publ. 22, Providence.

J.R. Bunch and D.J. Rose, eds. (1976): Sparse Matrix Computations.

Academic Press, New York.

W.K. Chen (1976): Applied Graph Theory (2nd ed.). North-Holland,

Amsterdam.

J.H. Christensen and D.F. Rudd (1969): Structuring design

computations. AIChE (American Institute of Chemical Engineers)

~, 12, 94-100.

D. Cobb (1984): Controllability, observability, and duality in

singular systems. IEEE Trans. Automatic Control, AC-29,

1076-1082.

J.P. Corfmat and A.S. Morse (1976): Structurally controllable and

structurally canonical systems. IEEE Trans. Automatic Control,

AC-21 , 129-131.

W.H. Cunningham (1984): Matroid partition and intersection algorithms.

Dept. Math. Stat., Carleton Univ.

W.H. Cunningham and A. Frank (1984): A primal-dual algorithm for

submodular flows. Math. Oper. Res., lQ, 251-262.

264 References

E.J. Davison (1977): Connectability and structural controllability of

composite systems. Automatica, 11, 109-113. A.L. Dulmage and N.S. Mendelsohn (1958): Coverings of bipartite

graphs. Canad. ~ Math., 12, 517-534. A.L. Dulmage and N.S. Mendelsohn (1959): A structure theory of

bipartite graphs of finite exterior dimension. Trans. of Royal

Soc. Canada, Section III, 21, 1-13.

A.L. Dulmage and N.S. Mendelsohn (1962): On the inversion of sparse

matrices. Math. Comp., 1£, 494-496.

A.L. Dulmage and N.S. Mendelsohn (1963): Two algorithms for bipartite

graphs. SIAM ~, 11, 183-194.

J. Edmonds (1965): Minimum partition of a matroid into independent

SUbsets. ~ Res. Nat. Bur. Stand., 69B, 67-72.

J. Edmonds (1967): Systems of distinct representatives and linear

algebra. ~ Res. Nat. Bur. Stand., 71B, 241-245.

J. Edmonds (1970): Submodular functions, matroids and certain

polyhedra. Combinatorial Structures and Their Applications (eds.

R. Guy et al.), Gordon and Breach, New York, 69-87.

J. Edmonds and R. Giles (1977): A min-max relation for submodular

functions on graphs. Ann. Disc. Math., 1, 185-204.

F.J. Evans and C. Schizas (1979): Digraph analysis of large-scale

systems: The system primitive. Electr. Lett., 12, 613-614.

S. Even and R.E. Tarjan (1975): Network flow and testing graph

connectivity. SIAM ~ Comput., ~, 507-518.

L.R. Ford, Jr., and D.R. Fulkerson (1962): Flows in Networks.

Princeton Univ. Press, Princeton.

0.1. Franksen, P. Falster and F.J. Evans (1979): Structural aspects of

controllability and observability --- I. Tensorial aggregation.

~ Franklin Inst., ~, 79-104.

0.1. Franksen, P. Falster and F.J. Evans (1979): Structural aspects of

controllability and observability --- II. Digraph decomposition.

~ Franklin Inst., ~, 105-124.

G. Fujisaki (1977): Field and Galois Theory lL ~ III (in Japanese).

Iwanami, Tokyo, 1977-1978.

S. Fujishige (1977): An algorithm for finding an optimal independent

linkage. ~ ~ Res. Soc. Japan, 20, 59-75.

S. Fujishige (1978): Algorithms for solving the independent-flow

problems. ~ Oper. Res. Soc. Japan, 21, 189-204.

S. Fujishige (1980): Principal structures of submodular systems.

Disc. ~ Math., ~, 77-79.

References 265

S. Fujishige, H. Rock and U. Zimmermann (1986): A strongly polynomial

algorithm for minimum cost submodular flow problem. Discussion

Paper Series 289, Inst. Socio-Economic Planning, Univ. Tsukuba.

F.R. Gantmacher (1959): The Theory of Matrices. Chelsea, New York.

M.R. Garey and D.S. Johnson (1979): Computers and Intractability --

A Guide to the Theory of NP-Completeness. Freeman, San Francisco.

A. George and J.W. Liu (1981): Computer ~olution of Large Positive

Definite Systems. Prentice-Hall, Englewood Cliffs.

K. Glover and L.M. Silverman (1976): Characterization of structural

controllability. IEEE Trans. Automatic Control, AC-21, 534-537.

I.C. Gokner (1976a): Controllability criteria using signal-flow

graphs. Int. ~ ~ Sci., 1, 65-74.

I.C. Gokner (1976b): A characterization of controllability suitable

for signal-flow graph applications. Int. ~ Syst. Sci., 1, 121-129.

F. Harary (1962): A graph-theoretic approach to matrix inversion by

partitioning. Numer. Math., A, 128-135.

R. Hassin (1982): Minimum cost flow with set-constraints. Networks,

.12.,1-21.

Y. Hayakawa and S. Hosoe (1982): On fixed modes of decentralized

control systems (in Japanese). Proc. 5th SICE ~ Dynamical

System Theory, December 1982, Yokosuka, 19-22.

Y. Hayakawa, S. Hosoe and M. Ito (1981): Dynamical degree and

controllability for linear systems with intermediate standard

form (in Japanese). Trans. Inst. Electr. Comm. Engin. Japan,

J64A, 752-759.

Y. Hayakawa, S. Hosoe, M. Hayashi and M. Ito (1981): Controllability

of structured systems with some linear dependence among variable

elements (in Japanese). Proc. 24th Conf. Japan Joint Automatic

Control, 1030, 59-60.

Y. Hayakawa, S. Hosoe, M. Hayashi and M. Ito (1982a): Structural

controllability of linear time-invariant compartmental systems

(in Japanese). Trans. Inst. Electr. Comm. Engin. Japan, J65A,

371-378.

Y. Hayakawa, S. Hosoe, M. Hayashi and M. Ito (1982b): A study of

structural identifiability of linear systems (in Japanese).

Trans. Soc. Instr. Control Engin., ~, 21-27.

Y. Hayakawa, S. Hosoe, M. Hayashi and M. Ito (1984): On the structural

controllability of compartmental systems. IEEE Trans. Automatic

Control, AC-29, 17-24.

266 References

E. Hellerman and D. Rarick (1971): Reinversion with the preassigned

pivot procedure. Math. Prog., 1, 195-216.

E. Hellerman and D. Rarick (1972): The partitioned preassigned

pivot procedure (P4 ). Sparse Matrices and Their Applications

(eds. D.J. Rose and R.A. Willoughby), Prenum Press, New York,

67-76.

D.M. Himmelblau (1966): Decomposition of large scale systems I.

Systems composed of lumped parameter elements. Chem. Engin.

Sci., ~, 425-438.

D.M. Himmelblau (1967): Decomposition of large scale systems --- II.

Systems containing nonlinear elements. Chem. Engin. Sci., 22,

883-895.

J.E. Hopcroft and R.M. Karp (1973): An n 5/ 2 algorithm for maximum

matchings in bipartite graphs. SIAM ~ Comput., ~, 225-231.

S. Hosoe (1980): Determination of generic dimension of controllable

subsystems and its applications. IEEE Trans. Automatic Control,

AC-25, 1192-1196.

S. Hosoe (1982): Controllability, observability and output regulation

of linear multi variable structured system. Proc. 11th SICE ~

Control Theory, May 1982, Kobe, 49-54.

S. Hosoe, Y. Hayakawa and T. Aoki (1984): Structural controllability

analysis for linear systems in linealy parameterized descriptor

form. IFAC World Congr., July 1984, Budapest, 14.3/D6, 115-119.

S. Hosoe and K. Matsumoto (1979): On the irreducibility condition in

the structural controllability theorem. IEEE Trans. Automatic

Control, AC-24, 963-966.

H.E. Huntley (1952): Dimensional Analysis. Macdonald & Co., London.

M. Ichikawa (1983): An Application of Matroid Theory to Systems

Analysis (in Japanese). Graduation thesis, Dept. Math. Eng.

Instr. Phy., Univ. Tokyo.

Information-Technology Promotion Agency (ITPA 1974): DPS User~s Manual

(in Japanese).

Information-Technology Promotion Agency, and Institute of the Japanese

Union of Scientists and Engineers (ITPA 1980): DPS (V2) User's

Manual (in Japanese).

Institute of the Japanese Union of the Scientists and Engineers (IJUSE

1976): JUSE-L-GIFS User's Manual, Ver. 3 (in Japanese).

M. Iri (1968): A min-max theorem for the ranks and term-ranks of a

class of matrices --- An algebraic approach to the problem of the

topological degrees of freedom of a network (in Japanese).

Trans. Inst. Electr. Comm. Engin. Japan, 51A, 180-187.

References 267

M. Iri (1969a): Network Flow, Transportation and Scheduling. Academic

Press, New York.

M. Iri (1969b): The maximum-rank minimum-term rank theorem for the

pivotal transforms of a matrix. Linear ~ Its ~, ~, 427-446.

M. Iri (1971): Combinatorial canonical form of a matrix with

applications to the principal partition of a graph (in Japanese).

Trans. Inst. Electr. Comm. Engin. Japan, 2k!, 30-37. (English

translation in Electronics and Communications in Japan, 2k! (1971),30-37.)

M. Iri (1978): A practical algorithm for the Menger-type

generalization of the independent assignment problem. Math. Prog.

Study, ~, 88-105.

M. Iri (1979): A review of recent work in Japan on principal

partitions of matroids and their applications. Ann. New York

Acad. Sci., ~, 306-319.

M. Iri (1981): Application of matroid theory to engineering systems

problems. Proc. Sixth Conf. Prob. Theory (eds. B. Bereanu et al.),

Editura Academiei Republicii Socialiste Romania, 107-127.

M. Iri (1983a): Applications of matroid theory. Mathematical

Programming --- The State of the Art (eds. A. Bachem,

M. Grotschel and B. Korte), Springer, Berlin, 158-201.

M. Iri (1983b): Application of matroid theory to systems analysis and

control. (Presented at RUTCOR's Inaugural Conf., Rutgers Univ.,

November 1983) Research Memorandum RMI 83-06, Dept. Math. Eng.

Instr. Phys., Univ. Tokyo.

M. Iri (1984a): Structural theory for the combinatorial systems

characterized by submodular functions. Progress in Combinatorial

Optimization (ed. W.R. Pulleyblank), Academic Press, 197-219.

M. Iri (1984b): Simultaneous computation of functions, partial

derivatives and estimates of rounding errors --- Complexity and

practicality. Japan ~ ~ Math., 1, 223-252.

M. Iri and S. Fujishige (1981): Use of matroid theory in operations

research, circuits and systems theory. Int. ~ ~ Sci., ~,

27-54.

M. Iri and T.-S. Han (1977): Linear Algebra (in Japanese). Kyoiku

Shuppan, Tokyo.

M. Iri and N. Tomizawa (1974): A practical criterion for the existence

of the unique solution in a linear electrical network with mutual

couplings (in Japanese). Trans. Inst. Electr. Comm. Engin. Japan,

57A, 599-605.

268 References

M. Iri and N. Tomizawa (1975a): A unifying approach to fundamental

problems in network theory by means of matroids. Electr. Comm.

Japan, 58A, 28-35.

M. Iri and N. Tomizawa (1975b): An algorithm for finding an optimal

"independent assignment". :L.:.. Oper. Res. Soc. Japan, .12., 32-57.

M. Iri, N. Tomizawa and S. Fujishige (1977): On the controllability

and observability of a linear system with combinatorial

constraints (in Japanese). Trans. Soc. Instr. Control Engin., 1},

235-242.

M. Iri, T. Tsuchiya and M. Hoshi (1985): Automatic computation of

partial derivatives and rounding-error estimates with

applications to large-scale systems of nonlinear equations (in

Japanese). :L.:.. Infor. Process. Soc. Japan, 26, 1411-1420.

M. Iri, J. Tsunekawa and K. Murota (1982): Graph-theoretic approach to

large-scale systems --- Structural solvability and block

triangularization (in Japanese). Trans. Infor. Process. Soc.

Japan, 23, 88-95. (English translation available: Research

Memorandum RMI 81-05, Dept. Math. Eng. Instr. Phy., Univ. Tokyo,

1981 • )

M. Iri, J. Tsunekawa and K. Yajima (1972): The graphical techniques

used for a chemical process simulator "JUSE GIFS". Information

Processing 11 (Proc. IFIP Congr. 71), Vo1.2, (Appl.), 1150-1155.

N. Jacobson (1964): Lectures in Abstract Algebra, III --- Theory of

Fields and Galois Theory. D. Van Nost~and, Princeton.

F.J. de Jong (1967): Dimensional Analysis for Economists.

Contributions to Economic Analysis 50, North-Holland.

T. Kailath (1980): Linear Systems. Prentice-Hall, Englewood Cliffs.

R.E. Kalman (1962): Canonical structure of linear dynamical systems.

Proc. Nat. Acad. Sci. (U.S.A.), ~, 596-600.

R.E. Kalman (1963): Mathematical description of linear dynamical

systems. SIAM:L.:.. Control, Ser.A, 1, 152-192.

K.V. Kim, Yu.E. Nesterov and B.V. Cherkasskii (1984): Ocenka

trudoemkosti vycislenija gradienta (in Russian). Doklady Akademii

Nauk SSSR, Matematika, 275, 1306-1309. (English translation: An

estimate of the effort in computing the gradient. Soviet Math.

Dokl., 29, 384-387.)

K.V. Kim, Iu.E. Nesterov, V.A. Skokov and B.V. Cherkasskii (1984):

Effektivnyi algoritm vycislenija proizvodnyh i ekstremalnye

zadaci (in Russian). Ekonomika i Matematiceskie Metody, 20,

309-318. (English translation: An efficient algorithm for

computing derivatives and extremal problems. Matekon, 21, 49-67.)

References 269

G. Kishi and Y. Kajitani (1968): Maximally distinct trees in a linear

graph (in Japanese). Trans. Inst. Electr. Comm. Engin. Japan,

.2..1!., 196-203.

H. Kobayashi and T. Yoshikawa (1982): Graph-theoretic approach to

controllability and localizability of decentralized control

systems. IEEE Trans. Automatic Control, AC-27, 1096-1108.

S. Kodama and M. Ikeda (1973): On representatIons of linear dynamical

systems (in Japanese). Trans. Inst. Electr. Comm. Engin. Japan,

J56-D, 553-560.

J.P.S. Kung (1978): Bimatroids and invariants. Advances Math., lQ, 238-249.

H.L. Langhaar (1951): Dimensional Analysis and Theory of Models. John

Wiley and Sons, New York.

E.L. Lawler (1975): Matroid intersection algorithms. Math. Prog., 2, 31-56.

E.L. Lawler (1976): Combinatorial Optimization: Networks and Matroids.

Holt, Rinehalt and Winston, New York.

E.L. Lawler and C.U. Martel (1982): Computing maximal 'polymatroidal'

network flows. Math. Oper. Res., 1, 334-347.

W. Lee, J.H. Christensen and D.F. Rudd (1966): Design variable

selection to simplify process calculations. AIChE (American

Institute of Chemical Engineers) ~, ~, 1104-1110.

W. Lee and D.F. Rudd (1966): On the ordering of recycles calculations.

AIChE (American Institute of Chemical Engineers) ~, ~,

1184-1190.

A. Lempel and I. Cederbaum (1966): Minimum feedback arc and vertex

sets of a directed graph. IEEE Trans. Circuit Theory, CT-13,

399-403.

C.-T. Lin (1974): Structural controllability. IEEE Trans. Automatic

Control, AC-19, 201-208.

A. Linnemann (1981): Decoupling of structured systems. ~ Control

Lett., 1, 79-86.

L. Lovasz and Y. Yemini (1982): On generic rigidity in the plane. SIAM

~ A1:.R.!. Disc. Meth., }, 91-98.

D.G. Luenberger (1977): Dynamic equations in descriptor form. IEEE

Trans. Automatic Control, AC-22, 312-321.

D.G. Luenberger (1978): Time-invariant descriptor systems. Automatica,

ti, 473-480.

H. Maeda (1981): On structural controllability theorem. IEEE Trans.

Automatic Control, AC-26, 795-798.

270 References

H. Maeda and T. Yamada (1979): Strong structural controllability.

SIAM ~ Control ~, 11, 123-138.

R.S.H. Mah (1982): Application of graph theory to process design and

analysis. Proc. Int. ~ Process ~~, 39-57.

T. Matsumoto and M. Ikeda (1983): Structural controllability based on

intermediate standard forms (in Japanese). Trans. Soc. Instr.

Control Engin., 12, 601-606.

M.M. Milic (1974): General passive networks Solvability,

degeneracies, and order of complexity. IEEE Trans. Circuits

~, CAS-21, 177-183.

K. Murota (1982a): Decomposition of a graph based on the Menger-type

linkings on it (in Japanese). Trans. Infor. Process. Soc. Japan,

n, 280-287.

K. Murota (1982b): Structural analysis of a large-scale system of

equations by means of the M-decomposition of a graph (in

Japanese). Trans. Infor. Process. Soc. Japan, 23, 480-486.

K. Murota (1982c): Menger-decomposition of a graph and its application

to the structural analysis of a large-scale system of equations.

Kokyuroku, Res. Inst. Math. Sci., Kyoto Univ., 422, 127-173.

To appear in Disc. A:02h Math.

K. Murota (1983a): LU-decomposition of a matrix with ~ntries of

different kinds. Linear ~ Its A:02h, 42, 275-283.

K. Murota (1983b): Structural controllability of a linear

time-invariant system with auxiliary variables (in Japanese).

Trans. Soc. Instr. Control Engin., 12, 104-109.

K. Murota (1983c): Structural Solvability and Controllability of

Systems. Doctor's dissertation, Dept. Math. Eng. Instr. Phys.,

Univ. Tokyo.

K. Murata (1983d): Structural controllability of a system with some

fixed coefficients (in Japanese). Trans. Soc. Instr. Control

Engin., 12, 683-690.

K. Murata (1984): Structural controllability of a system in descriptor

form expressed in terms of bipartite graphs (in Japanese). Trans.

Soc. Instr. Control Engin., 20, 272-274.

K. Murata (1985a): Use of the concept of physical dimensions in the

structural approach to systems analysis. Japan ~ ~ Math., ~,

471-494.

K. Murata (1985b): Combinatorial canonical form of layered mixed

matrices and block-triangularization of large-scale systems of

linear/nonlinear equations. Discussion Paper Series 257, Inst.

Socio-Economic Planning, Univ. Tsukuba.

References 271

K. Murota (1985c): Refined study on structural controllability of

descriptor systems by means of matroids. Discussion Paper Series

258, Inst. Socio-Economic Planning, Univ. Tsukuba. To appear in

SIAM h Control Q£.h

K. Murota and M. Iri (1983): Matroid-theoretic approach to the

structural solvability of a system of equations (in Japanese).

Trans. Infor. Process. Soc. Japan, ~, 157-164.

K. Murota and M. Iri (1985): Structural solvability of systems of

equations --- A mathematical formulation for distinguishing

accurate and inaccurate numbers in structural analysis of

systems. Japan h ~ Math., £, 247-271.

K. Murota, M. lri and M. Nakamura (1985): Combinatorial canonical form

of layered mixed matrices and its application to block

triangularization of systems of equations. To appear in SIAM h ~ Disc. Meth., ~ (1987), No.1.

M. Nakamura (1982a): Boolean sublattices connected with minimization

problems on matroids. Math. Prog., 22, 117-120.

M. Nakamura (1982b): Mathematical Analysis of Discrete Systems and Its

Applications (in Japanese). Doctor's dissertation, Dept. Math.

Eng. Instr. Phys., Univ. Tokyo.

M. Nakamura (1983): Analysis of discrete systems and its applications

(in Japanese). Trans. Inst. Electr. Comm. Engin. Japan, J66A,

368-373.

M. Nakamura and M. Iri (1979): Fine structures of matroid

intersections and their applications. Proc. Int. ~ Circuits

and Systems, Tokyo, 996-999.

M. Nakamura and M. Iri (1981): A structural theory for submodular

functions, polymatroids and polymatroid intersections. Research

Memorandum RMI 81-06, Dept. Math. Eng. Instr. Phys., Univ. Tokyo.

T. Ohtsuki, Y. Ishizaki and H. Watanabe (1968): Network analysis and

topological degrees of freedom (in Japanese). Trans. Inst.

Electr. Comm. Engin. Japan, 51A, 238-245.

Y. Oono (1960): Formal realizability of linear networks. Proc. ~

on Active Networks and Feedback Systems, Polytechnic Inst.

Brooklyn, New York, 475-486.

o. Ore (1955): Graphs and matching theorems. Duke Math. h, 22,

625-639.

T. Ozawa (1972): Order of complexity of linear active networks and

common tree in the 2-graph method. Electr. Lett., ~, 542-543.

T. Ozawa (1974): Common trees and partition of two-graphs (in

Japanese). Trans. Inst. Electr. Comm. Engin. Japan, 57A, 383-390.

272 References

T. Ozawa (1976a): Topological conditions for the solvability of linear

active networks. Int. ~ Circuit Theory and ~, k, 125-136.

T. Ozawa (1976b): Structure of 2-graphs (in Japanese). Trans. Inst.

Electr. Comm. Engin. Japan, J59A, 262-263.

T. Ozawa and Y. Kajitani (1979): Diagnosability of linear active

networks. IEEE Trans. Circuits ~, CAS-26, 485-489.

L. Pandolfi (1980): Controllability and stabilization for linear

systems of algebraic and differential equations. ~ ~ Theory

~, 30, 601-620.

C.H. Papadimitriou and K. Steiglitz (1982): Combinatorial

Optimization: Algorithms and Complexity. Prentice-Hall, Englewood

Cliffs.

B. Petersen (1979): Investigating solvability and complexity of linear

active networks by means of matroids. IEEE Trans. Circuits ~,

CAS-26, 330-342.

T.K. Pho and L. Lapidus (1973): Topics in computer-aided design,

part 1 --- An optimum tearing algorithm for recycle systems.

AIChE (American Institute of Chemical Engineers) ~, 12, 1170-1182.

J.C. Picard and M. Queyranne (1980): On the structure of all minimum

cuts in a network and applications. Math. Prog. Study, 11, 8-16.

S. Pissanetzky (1984): Sparse Matrix Technology. Academic Press,

London.

A. Recski (1979): Unique solvability and order of complexity of linear

networks containing memoryless n-ports. Int. J. Circuit Theory

and ~, 1, 31-42.

A. Recski (1980): Sufficient conditions for the unique solvability of

linear memoryless 2-ports. Int. J. Circuit Theory and ~, ~,

95-103.

A. Recski (1986): Matroid Theory and Its Applications. Springer,

Berlin.

A. Recski and M. Iri (1980): Network theory and transversal matroids.

Disc. ~ Math., z., 311-326.

H.H. Rosenbrock (1970): State-Space and Multivariable Theory. Nelson,

London.

H.J. Ryser (1973): Indeterminates and incidence matrices. Linear

Multilinear ~, 1, 149-157.

R.W.H. Sargent (1978): The decomposition of systems of procedures and

algebraic equations. Numerical Analysis (Proc. Biennial Conf.,

Dundee, 1977, ed. G.A. Watson), Lecture Notes in Mathematics,

630, Springer, Berlin, 158-178.

References 273

C. Schizas and F.J. Evans (1980): Rank invariant transformations and

the controllability of large-scale systems. Electr. Lett., 1£, 19-20.

C. Schizas and F.J. Evans (1981): A graph theoretic approach to

multivariable control system design. Automatica, 11, 371-377.

P. Schonsleben (1980): Ganzzahlige Polymatroid-Intersektions

Algorithmen. Dissertation, Eidgenossische Technische Hochschule

Zurich, Zurich.

A. Schrijver (1978): Matroids and Linking Systems. Math. Centre Tracts

88, Amsterdam.

D.J.G. Sebastian, R.G. Noble, R.K.M. Thambynayagam and R.K. Wood

(1981): DPS --- A unique tool for process simulation. Proc. 2nd

World Congr. Chemical Engin., Montreal, y, 473-480.

M.E. Sezer and D.D. Siljak (1981): On structural decomposition and

stabilization of large-scale control systems. IEEE Trans.


R.W. Shields and J.B. Pearson (1976): Structural controllability of

multiinput linear systems. IEEE Trans. Automatic Control, AC-21,

203-212.

M. Spivak (1965): Calculus on Manifolds, Benjamin, New York.

D.V. Steward (1962): On an approach to techniques for the analysis of

the structure of large systems of equations. SIAM Review, ~,

321-342.

D.V. Steward (1965): Partitioning and tearing systems of equations.

SIAM ~ Numer. Anal., Series B2, 345-365.

N. Suda (1980): Structural aspects of system and control theory --

Introduction (in Japanese). Proc. 19th Conf. Soc. Instr. Control

Engin., 12, 349-350.

K. Sugihara (1981): Program system for the principal partition of a

bipartite graph --- Reference manual. Research Memorandum RMI

81-03, Dept. Math. Eng. Instr. Phy., Univ. Tokyo.

K. Sugihara (1982a): Mathematical structures of line drawings of

polyhedrons --- Towards man-machine communication by means of

line drawings. IEEE Trans. Pattern Anal. Mach. Intel., PAMI-4,

458-469.

K. Sugihara (1982b): Detection of structural inconsistency in systems

of equations with internal degrees of freedom (in Japanese).

Trans. Inst. Electr. Comm. Engin. Japan, J65A, 911~918.

K. Sugihara (1985): Detection of structural inconsistency in systems

of equations with degree of freedom and its applications. Disc.

~ Math. lQ, 297-312.

274 References

T. Takamatsu, I. Hashimoto and S. Tomita (1982): Structural analysis

of algebraic equations with the use of directed graphical

representation (in Japanese). Kagaku Kogaku Ronbunshu, ~, 500-506.

R.K.M. Thambynayagam, R.K. Wood and P. Winter (1981): DPS --- An

engineer's tool for dynamic process analysis. The Chemical

Engineer, 222, 58-65.

N. Tomizawa (1976): Strongly irreducible matroids and principal

partition of a matroid into strongly irreducible minors (in

Japanese). Trans. Inst. Electr. Comm. Engin. Japan, J59A, 83-91.

N. Tomizawa and S. Fujishige (1982): Historical survey of extensions

of the concept of principal partition and their unifying

generalization to hypermatroids. Systems Science Research Report,

No.5, Dept. System Sci., Tokyo Inst. Technology.

N. Tomizawa and M. Iri (1974a): An algorithm for determining the rank

of a triple matrix product AXB with application to the problem of

discerning the unique solution in a network (in Japanese). Trans.

Inst. Electr. Comm. Engin. Japan, 57A, 834-841. (English

translation in Electronics and Communications in Japan, 57A

(1974), 50-57.)

N. Tomizawa and M. Iri (1974b): An algorithm for solving the

"independent assignment problem" with application to the problem

of determining the order of complexity of a network (in Japanese).

Trans. Inst. Electr. Comm. Engin. Japan, 57A, 627-629.

C.A. Tovey and M.A. Trick (1983): An 0(m4d) algorithm for the maximum

polymatroidal flow problem. School Indust. Syst. Eng., Georgia

Inst. Technology.

G.C. Verghese, B.C. Levy and T. Kailath (1981): A generalized

state-space for singular systems. IEEE Trans. Automatic Control,

AC-26, 811- 831.

B.L. van der Waerden (1955): Algebra. Springer, Berlin.

D.J.A. Welsh (1970): On matroid theorems of Edmonds and Rado. J.

London Math. Soc., ~, 251-256.

D.J.A. Welsh (1976): Matroid Theory. Academic Press, London.

W.A. Wolovich (1974): Linear Multivariable Systems. Springer, New York.

W.M. Wonham (1979): Linear Multivariable Control: ! Geometric

Approach. Springer, New York.

K. Yajima and J. Tsunekawa (1982): Graphical techniques used for a

dynamic chemical process simulation. System Modeling and

Optimization (Proe. 10th IFIP Conf., New York City, 1981; eds.

R.F. Drenick and F. Kozin), Lecture Notes in Control and

Information Sciences, 38, Springer, Berlin, 826-833.

References 275

K. Yajima, J. Tsunekawa and S. Kobayashi (1981): On equation-based

dynamic simulation. Proc. 2nd World Congr. Chemical ~,

Montreal, y. K. Yajima, J. Tsunekawa, H. Shono, S. Kobayashi and D.J. Sebastian

(1982): On graph-theoretic techniques for large-scale process

systems. Int. Symp. Process Syst. Engin., Kyoto, August 1982.

T. Yamada and D.G. "Luenberger (1985a): Generic properties of column

structured matrices. Linear ~ Its ~, 65, 189-206.

T. Yamada and D.G. Luenberger (1985b): Generic controllability theorem

for descriptor systems. IEEE Trans. Automatic Control, AC-30,

144-152.

T. Yamada and D.G. Luenberger (1985c): Algorithms to verify generic

causality and controllability of descriptor systems. IEEE Trans.


E.L. Yip and R.F. Sincovec (1981): Solvability, controllability, and

observability of continuous descriptor systems. IEEE Trans.


R.M. Zazworsky and H.K. Knudsen (1978): Controllability and

observability of linear time-invariant compartmental models.

IEEE Trans. Automatic Control, AC-23, 872-877.

Subject Index

A

Accurate number, 122

Admi ttance, 191

Algebraic

--- element, 7

--- matroid, 20

Algebraically independent, 7

Arc

admissible 10

efficient ---, 10

Associated bipartite graph

[graph], 13

[matrix], 8

Assumption

AO, 143

--- A1, 134

--- A2, 145

basic ---, 31

generality

generality

generality

GA 1, 36

GA2, 131

GA3, 131

Auxiliary network, 25

B

Base

[matroid], 16

[polymatroid], 19

Basic assumption, 31

Bipartite graph, 9

--- associated with a

graph, 13

--- associated with a

matrix, 8

Block-triangularization, 28

C

Canonical quasi-diagonal form, 94

Capacitated network, 13

Circuit, 16

fundamental

Closure, 16

16

Coates graph, 87

Coloop, 16

Combinatorial canonical

decomposition, 119

Combinatorial canonical form, 179

Component

--- network, 42

DM- --, 10

effective ---, 46

ineffective 46

L- --, 41

L-irreducible

M- ---, 46

M-irreducible

strong ---, 9

strongly connected

41

46

Computational graph, 33

Condition

C1 , 94 C2, 95

C3, 95

C4, 96

MO, 235

M1, 233

M2, 233

M3, 238

Connector, 46

Consistent part

[DM-decomposition], 12

[M-decomposition], 46

Contraction, 17

Controllability, 92

C- --, 95

9

--- of exponential mode, 95

modal --- matrix, 94

R- -, 95

structural 99

Controllable, 92, 95

-- subset, 117

structurally

Cost, 24 99

Direct sum, 17

DM-decomposition, 10

DPS, 28

Dulmage-Mendelsohn

decomposition, 10

Dynamic graph, 113

Cover, 9 Dynamical degree, 95, 226

minimum 9

Covered E

[matching], 9 Effective vertex, 44

[partial order], 6

Current-graph, 182

Cut

[capacitated network], 13

-- capacity, 25

Cycle

essential --, 65

D

Decomposition

Entrance

[auxiliary graph of

matching],10

[graph], 14

Essential cycle, 65

Essential unknown, 62

Exit

[auxiliary graph of

matching],10

[graph], 14

combinatorial canonical --, 119 Extended form, 86

--- by minimum covers of

admittance matrix, 192

--- principle for submodular

function, 22

DM- --, 10

Dulmage-Mendelsohn

Kalman's canonical

L- --, 41

min-cut

Deg-ree

43

--- of transcendency, 7

dynamical ---, 95, 226

Dependence function, 19

Dependent set, 16

10

116

Descriptor form, 86

Dimensional analysis, 136

Dimensional formula, 136

Dimensional homogeneity, 137

Dimensioned matrix, 138

F

Feedback vertex set, 62

Fixed mode, 256

Flow, 14

graph, 87

independent ---, 24

optimal ---, 24

Form I, 97

Free matroid, 20

Fundamental circuit, 16

G

Gammoid, 20

Generality assumption

GA1, 36

-- GA2, 131

- GA3, 131

Generic-rank, 8

Index 277

278 Index

Graph

Coates 87

computational ---, 33 current- ---, 182

dynamic ---, 113

flow ---, 87

Mason ---, 87

representation 33

J

Jacobian matrix, 30

JUSE-GIFS, 28

K

Kalman's canonical

decomposition, 116

signal-flow ---, 87 L

voltage- ---, 182 L-decomposition, 41

H

Horizontal tail

[combinatorial canonical

form], 179


Hybrid immittance matrix, 221

I

Ideal, 23

Immittance matrix, 221

Impulse mode, 95

Inaccurate number, 122

Inconsistent part



Independence polyhedron, 19

Independent-assignment

problem, 25

Independent flow, 24

maximum ---, 24

Independent-flow problem, 24

Independent-matching problem, 25

Independent set, 16

Independent vector, 19

Ineffective component, 46

Ineffective vertex, 44

Inherent unknown, 56

Intersection, 18

Irreducibility, 97

Layered mixed matrix, 133

combinatorial canonical form

of ---, 179

Left-hand-side variable, 73

Lindemann-Weierstrass theorem, 7

Linear matroid, 20

Linkage lemma, 37

Linking

complete 14

--- function, 21

maximum ---, 14

Menger-type ---, 14

Linking system, 21

deltoid 22

gammoid 22

LM-equivalent, 174

Loop, 16

M

M-decomposition

[associated network], 47

[graph], 46

Mason graph, 87

Matching, 9

complete ---, 10

covered by a ---, 9 independent ---, 25

maximum ---, 10

Matrix

admittance 191

dimensioned --, 138

hybrid immittance --, 221

immittance --, 221

layered mixed --, 133

-- net, 252

mixed --, 132

physical --, 143

system --, 221

strictly upper triangular

--, 198

totally unimodular --, 139

Matroid, 16

algebraic

free --, 20

linear --, 20

20

-intersection problem, 18

-- -partition problem, 18

transversal --, 20

weighted -- -partition

problem, 18

Matroidal polymatroid, 19

Max-flow min-cut theorem, 14

Maximal inconsistent part



Maximum matching, 10

Menger-type linking, 14

Menger's theorem, 15

Minimal inconsistent part



Minimum separator, 14

Mixed matrix, 132

eigenvalue of a --, 220

Modal controllability matrix, 94

Mode

exponential --, 95

fixed --, 256

impulse --, 95

Mul tiport, 195

N

Network

auxiliary 25

capacitated --, 13

component --, 43

Index 279

-- associated with a graph, 14

Newton method, 201, 213

Number

accurate --, 122

inaccurate --, 122

two kinds of --, 122

o Observability, 116

Observable, 116

-- subset, 118

Operation definition, 73

Optimal flow, 24

Order ideal, 23

p

Partial derivative, 30

Physical dimension, 136

Physical matrix, 142

Polymatroid, 18

matroidal --, 19

Principal partition of

M (Q) * AM (T), 183

R

Rank

[matrix], 7

[matroid], 16

generic --, 8

-- function, 16, 18

-- identity, 149

term --, 7

Reachability

[dynamical system], 95

[graph], 9

280 Index

Reachable


[graph], 9

Reaction formula, 128

Reduced system, 62

Regular pencil, 94

Representation graph, 33

Re striction, 17

Right-hand-side variable, 73

s s-arc, 103

Saturation function, 19

Separa tor, 14

minimum --, 14

Solvabili ty

structural --, 31

Standard canonical form, 94

Standard form


[system definition), 73

[system of equations], 29

State-space equation

in descriptor form, 86

in extended form, 86

in standard canonical

form, 94

in standard form, 85

Stem, 100

Stoichiometric coefficient, 128

Strictly upper triangular, 198

Strong component, 9

Strongly connected component, 9

Structural controllability, 99

Structural solvability, 31

Structurally controllable, 99

Structurally solvable, 31

Structured system, 99

Submodular function, 16

decomposition principle

for --, 22

Submodularity, 16

System definition, 73

System matrix, 221

T

Tail

horizontal


form], 179


vertical -


form], 179


Term-rank, 7

Total unimodularity, 139

Transcendental, 7

Transversal matroid, 20

Type

U

Union

<A>, 74 <DD>, 62

<G>, 74 <R>, 75 <S>, 74

[linking system], 22

[matroid], 17

Unknown

essential --, 62

inherent --, 56

V

Value

of a flow, 14

of an independent flow, 24

Variable

left-hand-side 73

right-hand-side ---, 73

of type <A>, 74

of type <DD>, 62 of type <G>, 74

of type <R>, 75

of type <8>, 74 Vertex

effective 44 ineffective ---, 44

maximal 9

minimal ---, 9

Vertical tail


form], 179


Voltage-graph, 182

Index 281

references - springer978-3-642-61586-3/1.pdf · 264 references e.j. davison (1977): connectability...

Documents