modern sliding mode control theory
TRANSCRIPT
Lecture Notesin Control and Information Sciences 375
Editors: M. Thoma, M. Morari
Giorgio Bartolini, Leonid Fridman,Alessandro Pisano, Elio Usai (Eds.)
Modern Sliding Mode ControlTheoryNew Perspectives and Applications
ABC
Series Advisory BoardF. Allgöwer, P. Fleming, P. Kokotovic,A.B. Kurzhanski, H. Kwakernaak,A. Rantzer, J.N. Tsitsiklis
EditorsGiorgio BartoliniDepartment of Electrical andElectronic Engineering(DIEE), University of Cagliari, Piazzad’Armi, 09123, Cagliari (Italy)E-Mail: [email protected]
Leonid FridmanDepartment of Control, EngineeringFaculty, National Autonomous Universityof Mexico (UNAM), 04510,Mexico, D.F., MexicoE-Mail: [email protected]
Alessandro PisanoDepartment of Electrical and ElectronicEngineering (DIEE), Universityof Cagliari, Piazza dŠArmi, 09123,Cagliari (Italy)E-Mail: [email protected]
Elio UsaiDepartment of Electrical and ElectronicEngineering (DIEE), Universityof Cagliari, Piazza d’Armi, 09123,Cagliari (Italy)E-Mail: [email protected]
ISBN 978-3-540-79015-0 e-ISBN 978-3-540-79016-7
DOI 10.1007/978-3-540-79016-7
Lecture Notes in Control and Information Sciences ISSN 0170-8643
Library of Congress Control Number: 2008923754
c© 2008 Springer-Verlag Berlin Heidelberg
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To my wife Irene, to my mother Lucia,and to the memory of my father Giovanni. A.P.
Preface
This book is a collection of invited chapters covering several areas of modernsliding mode control theory. Preparing this book we tried to identify key con-tributions defining the theoretical and applicative state of the art of the slidingmode control theory and the most promising trends of the ongoing researchactivities.
The contributions is divided in four main parts:
Part I: Basic Theory.Part II: Design MethodsPart III: Observers and Fault DetectionPart IV: Applications
The first part of the book (Part I: Basic Theory) is devoted to a collection ofsix mostly theoretical chapters addressing basic theoretical issues of sliding-modebased control systems.
The first Chapter, by Giorgio Bartolini, Elisabetta Punta, and Tullio Zolezzi,presents new definitions of approximability for nonlinear second order slidingmode control systems including the comparison with the related known prop-erties for first order sliding mode control methods. Sufficient conditions are ob-tained for second-order regularization, a sliding motion error estimate is derived,and some relevant examples are discussed.
Chapter 2, by Igor Boiko, Leonid Fridman, Alessandro Pisano, and Elio Usai,develops a systematic approach to the chattering analysis in systems with secondorder sliding modes. Sufficient conditions for the existence of orbitally stableperiodic motions are found in terms of the properties of corresponding Poincaremaps. For linear systems driven by the second-order SMC “Generalized Sub-Optimal” algorithm, analysis tools based on the frequency-domain methods aredeveloped. Examples of analysis, worked examples, and simulation results aregiven throughout the Chapter.
Chapter 3, by Igor Boiko, studies sliding mode systems containing parasiticdynamics. A model of the chattering behaviour, and a full-order model of theaveraged motions having the same order of the original system, are obtained via
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the use of the locus of a perturbed relay system (LPRS) method. The possibilityof shaping of the plant frequency characteristic in order to achieve the desiredfrequency of chattering and to enhance the closed-loop performance is exploredin the chapter.
The fourth Chapter, by Arie Levant and Lela Alelishvili, deals with a surveyof the most recent developments of homogeneity-based higher-order SMC the-ory. The “black-box” control problem, where the systems input-output relativedegree is the unique available prior information for the controller design, is dealtwith, and several solutions are recalled. The ”Nested” and ”Quasi-continuous”arbitrary-order sliding mode controllers are described. Next the output-feedbacksliding-mode control problem is tackled via the combined use of the arbitrary-order SMC algorithms and finite time converging exact differentiators. Theprinciples and applications of high-order integral sliding mode control is finallydiscussed.
Chapter 5 by Yaodong Pan and Katsuhisa Furuta deals first with the de-sign of a second-order invariant PR-sliding sector for continuous time systems.A quadratically stable sector-based VS control system is proposed, where an“inner” and “outer” sectors are introduced to let the control law be continuousand more easily implementable in practice. The proposed VS control algorithmis applied to control an inverted pendulum control system.
Chapter 6 by Zbigniew Galiasa and Xinghuo Yu, performs a complete anal-ysis of discretization behaviors of some Equivalent Control Based (ECB) SMCsystems with relative degree higher than one using the Euler’s discretization.Former results for Euler-discretized ECB-SMC systems with relative degree oneare reviewed. This paves the way to study the ECB-SMC systems with relativedegree higher than one. Some theoretical results for the Euler’s discretization ofECB-SMC systems with relative degree one are used to analyse the ECB-SMCsystems with arbitrary relative degree. The chapter is concluded by some com-parisons with the existing results on continuous-time high-order SMC systems,where certain commonalities are observed.
The second part of the book (Part II: Design Methods) is a collection ofchapters covering recent design techniques addressing SMC problems for spe-cific, challenging, classes of systems. This part contains a number of combinedapproaches merging different approaches (e.g., homogeneity-based, flatness andbackstepping, fractional-order controllers) and SMC techniques.
In the Chapter 7, by Christopher Edwards, Thierry Floquet, and Sarah Spur-geon, the classical restriction of sliding mode design approaches, namely to as-sume that the transfer function matrix between the driving signal and the mea-sured output of interest must be minimum phase and relative degree one, isstudied. The chapter demonstrates that the relative degree condition can beweakened if the nominal linear system used for the controller or observer designis combined with sliding-mode exact differentiators. Similar approach is also ex-ploited for improved unknown-input reconstruction scheme. Simulation resultsfor a ninth order nonlinear system which does not satisfy the usual relativedegree one condition are presented.
Preface IX
In the Chapter 8, by Simon Baev, Yuri Shtessel, and Ilya Shkolnikov, asymp-totic output tracking in a class of causal nonminimum-phase uncertain nonlinearsystems is addressed via higher order sliding mode approach. Local asymptoticstability of the output tracking-error dynamics is provided. An output referenceprofile and an external disturbance forcing the internal dynamics are defined byan unknown linear exosystem. The input-output dynamics is compensated byhigher order sliding mode (HOSM) control. A numerical example illustrates theperformance of the developed HOSM control algorithm.
Chapter 9, by Isaac Chairez, Alexander Poznyak and Tatiana Poznyak, dealswith the, so-called, neuro-tracking-control for a class of uncertain nonlinear dy-namic systems subject to state and output external perturbations. Differentialneural networks (DNN) are used to design the black-box nonlinear observer.Then, an adaptive (output based) HOSM controller using the current state es-timate is suggested to realize the desired tracking process. A second-order me-chanical system and a water ozonation process are considered as the illustrativeexamples.
Chapter 10 by Hebertt Sira Ramırez and Vicente Feliu-Battle considers thecontrol of a special class of Single Input Single Output (SISO) switched fractionalorder systems (SFOS) from the viewpoints of the Generalized Proportional In-tegral (GPI) control and sliding mode based modulator. Additionally, a PulseWidth Modulation (PWM) duty ratio synthesis approach is developed for theapproximate discontinuous control of the same class of systems. A fractional-order GPI controller is proposed which transforms the average model of thesystem into a “classical”, integer order, chain of integrators, with desired closedloop dynamics thus achieved through a classical compensation network robustlyacting in the presence of constant load perturbations. An illustrative simulationexample dealing with an electric radiator system is presented.
In the Chapter 11 by Antonella Ferrara, Luisa Giacomini, and Claudio Vec-chio, a class of nonholonomic systems in chained form, affected by uncertainnonlinear drift term and parametric uncertainties, is addressed. The proposeddesign methodology is based on a suitable transformation of the system model,so that, on the basis of the transformed system state, it is possible to designa particular sliding manifold and an appropriate parameter adaptation mech-anism as well as to re-formulate the control problem as a second order slidingmode control problem. The capability of the proposed control law in dealingwith unmatched parametric uncertainties, in contrast to previous proposals, isdemonstrated.
Chapter 12 by Jian-Xin Xu and Khalid Abidi considers the output tracking ofa minimum-phase linear system subject to matched time varying disturbances.To accomplish the task of arbitrary reference tracking three approaches, basedon discrete-time integral sliding mode (ISMC), will be considered: 1) State Feed-back, 2) Output Feedback, and 3) Output Feedback with a State Observer. Theproposed schemes allow full control of the closed-loop error dynamics and theelimination of the reaching phase. It is worth to highlight that the discrete-time
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ISMC can achieve the O(T 2) boundary for output tracking error even in thepresence of O(T ) accuracy in the state estimation.
Chapter 13 by Ali J Koshkouei, Keith Burnham, and Alan Zinober, inves-tigates some connections between adaptive backstepping, flatness and slidingmode control. A combined technique using SMC and backstepping is presentedto control a class of nonlinear uncertain perturbed systems which can be trans-formed into a parametric semi-strict feedback form. The concept of differentialflatness and its exploitation in SMC design problems are also considered. Themain advantages and limitations of backstepping, flatness and SMC are discussedby means of a simulation example.
The third part of the book (Part III: Observers and Fault detection) concen-trates on the topics of state observation and observer-based fault detection forsome classes of inear and nonlinear processes. Both theoretical and applicativechapters are contained in this part of the book.
In the Chapter 14 by Leonid Fridman, Arie Levant, and Jorge Davila algo-rithms for observation, identification and fault detection of linear time-invariantstrongly observable systems with unknown inputs are developed, based on highorder sliding modes. The possibility of their extension to strongly detectable andnonlinear systems is discussed. Some applications of the proposed algorithms arepresented.
In the Chapter 15, by Mehrdad Saif, Weitian Chen, and Qing Wu, the devel-opment of high order sliding mode observers and differentiator design strategiesis reviewed. The design of a second order sliding mode observer and an high-order sliding mode differentiator is presented for state estimation in a class ofnonlinear systems and for the real-time estimation of the derivatives of a signalfunction, respectively. Next, the proposed second order observer and the highorder differentiators are applied together to fault diagnosis problems in systemswith relative degree higher than one, and fault diagnosis schemes are constructed.Finally, two examples of application to fault diagnosis problems for uncertainsystems are presented.
Chapter 16 by Hassan Shraim, Mustapha Ouladsine, and Leonid Fridmanconcerns vehicle parameter and states estimation problems which are addressesvia Sliding Mode Observers. The main contributions of the chapter resides inthe estimation of the wheel contact forces with the ground, side slip angle andthe velocity of the vehicle. Those estimations avoid the use of expensive sensorsand allows to preview some critical situations that may occur while driving, suchas excessive rotation around Z axis, excessive side slipping, inappropriate lateralacceleration. The proposed observers are simple to implement and guaranteefast convergence and robustness. They are validated by means of a high-orderhighly detailed vehicle simulator previously developed. The analysis covers mostof the driving cases, such as a double lane trajectory, straight line motion withsignificant acceleration and deceleration, fast changes in the steering angle.
The last Chapter 17, by Vincent Lebastard, Yannich Aoustin, Frank Plestan,and Leonid Fridman, suggests an alternative to the measurement of five-linksbiped robot absolute orientation, namely its estimation based on high order
Preface XI
sliding mode observers. The measurement of the absolute orientation for a walk-ing biped robot in imbalance phases is quite delicate. A solution for the esti-mation of the absolute orientation is proposed. The observer is based on a highorder sliding mode differentiator, which has been chosen for its robustness, ac-curacy and finite-time convergence features. Stability analysis of observer-basedcontrol law and experimental results on the RABBIT biped robot prototype aredisplayed.
The final, fourth part of the book (Part IV: Applications) presents some ap-plicative chapters covering practical engineering control problems dealt with bymeans of the sliding mode approach.
In the Chapter 18 by Yuri Orlov, Luis T. Aguilar, Leonardo Acho, and AdanOrtiz , orbital stabilization of a simple underactuated manipulator, namely, two-link pendulum robot (Pendubot) is under study. The quasi-homogeneous controlsynthesis is utilized to design a switched controller that drives the actuated linkof the Pendubot to a periodic reference orbit in finite time. A modified Van derPol oscillator is involved into the synthesis as an asymptotical generator of theperiodic motion. The resulting closed-loop system is capable of moving from oneorbit to another by simply changing the parameters of the modified Van derPol oscillator. Performance issues of the proposed synthesis are illustrated in anexperimental study of the swing up/balancing control problem of moving thePendubot from its stable downward position to the unstable inverted position.
Chapter 19 by Alexander Loukianov, Leonid Fridman, Jose Canedo, EdgarSanchez, and Adolfo Soto-Cota, considers the combination of the block con-trol principle and SM control techniques. A class of nonlinear minimum phaseSISO systems presented in nonlinear block controllable (NBC) form, that modelsboth the plant and actuator dynamics, is presented. Considering the completeplant and actuator dynamics, the block control technique is first used to suit-ably design the nonlinear sliding manifold, and the First Order Sliding Mode(FOSM) algorithm is implemented to ensure finite time convergence to the de-signed sliding manifold. Then a lower-order sliding manifold is designed basedon the plant dynamics only, and a High Order Sliding Mode (HOSM) algorithmis implemented to achieve chattering free motion of the closed-loop system in thepresence of the actuator unmodeled dynamics. The proposed method is appliedto design robust controller for a power electric system in presence of the excitersystem unmodeled fast dynamics. Finally neural network based second order SMblock control for an electro-hydraulic system in presence of the electric actuatorunmodeled dynamics is studied.
Chapter 20 by Parisa Kaveh and Yuri Shtessel, studies the application of high-order SMC techniques to feedback-based glucose regulation in treatment of Dia-betes. In the chapter, some higher order sliding mode control techniques are con-sidered for the cascade robust stabilization of the glucose concentration level of adiabetic patient in presence of the parameter variations and meal disturbance. Inthe inner loop super-twisting control stabilizes the glucose pump-actuator. In theouter loop, the higher order sliding mode controller generates a command to thepump-actuator in terms of insulin injection rate. The efficiency of the proposed
XII Preface
controllers together with the required HOSM based observers/differentiators, i.e.robustness and high accuracy, is confirmed via simulations.
The concluding Chapter 21 by Alessandro Pisano and Elio Usai studies thecontact force regulation problem in active pantographs for high-speed trans-portation systems. One of the main problems in high-speed-train transportationsystems is indeed related to the current collection quality, that can dramaticallydecrease because of oscillations of the pantograph-catenary system. In the chap-ter some results about the possible implementation of Variable Structure Control(VSC) techniques on a wire-actuated symmetric pantograph are presented. Re-cent results about the frequency-based analysis of VSC systems featuring second-order sliding modes are exploited to avoid the performance-destroying effect ofthe resonant wire actuator and to get a continuous control force without usingobservers. Simulations show that the contact force results to be satisfactorilyclose to the desired set-point also in the presence of measurement noise.
Cagliari, January 2008 Giorgio BartoliniMexico City, January 2008 Leonid FridmanCagliari, January 2008 Alessandro PisanoCagliari, January 2008 Elio Usai
Contents
Part I: Basic Theory
Regularization of Second Order Sliding Mode Control SystemsGiorgio Bartolini, Elisabetta Punta, Tullio Zolezzi . . . . . . . . . . . . . . . . . . . . . 3
A Comprehensive Analysis of Chattering in Second OrderSliding Mode Control SystemsIgor Boiko, Leonid Fridman, Alessandro Pisano, Elio Usai . . . . . . . . . . . . . 23
Analysis of Closed-Loop Performance and Frequency-DomainDesign of Compensating Filters for Sliding Mode ControlSystemsIgor Boiko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Discontinuous Homogeneous ControlArie Levant, Lela Alelishvili . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Second-Order Sliding Sector for Variable Structure ControlYaodong Pan, Katsuhisa Furuta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
On Euler’s Discretization of Sliding Mode Control Systemswith Relative Degree RestrictionZbigniew Galias, Xinghuo Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Part II: Design Methods
Circumventing the Relative Degree Condition in Sliding ModeDesignChristopher Edwards, Thierry Floquet, Sarah Spurgeon . . . . . . . . . . . . . . . . 137
HOSM Driven Output Tracking in the Nonminimum-PhaseCausal Nonlinear SystemsSimon Baev, Yuri B. Shtessel, Ilia Shkolnikov . . . . . . . . . . . . . . . . . . . . . . . . 159
XIV Contents
High Order Sliding Mode Neurocontrol for UncertainNonlinear SISO Systems: Theory and ApplicationsIsaac Chairez, Alexander Poznyak, Tatyana Poznyak . . . . . . . . . . . . . . . . . . 179
A Generalized PI Sliding Mode and PWM Control ofSwitched Fractional SystemsHebertt Sira Ramırez, Vicente Feliu Battle . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Stabilization of Nonholonomic Uncertain Systems ViaAdaptive Second Order Sliding Mode ControlAntonella Ferrara, Luisa Giacomini, Claudio Vecchio . . . . . . . . . . . . . . . . . . 223
Output Tracking with Discrete-Time Integral Sliding ModeControlXu Jian-Xin, Khalid Abidi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Flatness, Backstepping and Sliding Mode Controllers forNonlinear SystemsAli J. Koshkouei, Keith Burnham, Alan Zinober . . . . . . . . . . . . . . . . . . . . . . 269
Part III: Observers and Fault Detection
Observation and Identification Via High-Order Sliding ModesLeonid Fridman, Arie Levant, Jorge Davila . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
High Order Sliding Mode Observers and Differentiators–Application to Fault Diagnosis ProblemMehrdad Saif, Weitian Chen, Qing Wu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Vehicle Parameter and States Estimation Via Sliding ModeObserversHassan Shraim, Mustapha Ouladsine, Leonid Fridman . . . . . . . . . . . . . . . . . 345
An Alternative to the Measurement of Five-Links BipedRobot Absolute Orientation: Estimation Based on High OrderSliding ModeVincent Lebastard, Yannick Aoustin, Franck Plestan, Leonid Fridman . . . 363
Part IV: Applications
Robust Orbital Stabilization of Pendubot: AlgorithmSynthesis, Experimental Verification, and Application toSwing up and Balancing ControlYuri Orlov, Luis T. Aguilar, Leonardo Acho, Adan Ortiz . . . . . . . . . . . . . . . 383
Contents XV
Higher Order SM Block-Control of Nonlinear Systems withUnmodeled Actuators: Application to Electric Power Systemsand Electrohydraulic Servo-DrivesAlexander G. Loukianov, Leonid Fridman, Jose M. Canedo,Edgar Sanchez, Adolfo Soto-Cota . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
Blood Glucose Regulation Via Double Loop Higher OrderSliding Mode Control and Multiple Sampling RateParisa Kaveh, Yuri B. Shtessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
Contact Force Regulation in Wire-Actuated PantographsAlessandro Pisano, Elio Usai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
List of Contributors
Khalid AbidiDepartment of Electrical andComputer Engineering, NationalUniversity of Singapore, 4 EngineeringDrive 3, Singapore [email protected]
Leonardo AchoCentro de Investigacion y Desarrollode Tecnologıa Digital, CITEDI-IPN,2498 Roll Dr. #757, Otay Mesa, SanDiego, CA, [email protected]
Luis AguilarCentro de Investigacion y Desarrollode Tecnologıa Digital, CITEDI-IPN,2498 Roll Dr. #757, Otay Mesa, SanDiego, CA, [email protected]
Lela AlelishviliApplied Mahematics Department,Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, [email protected]
Yannick AoustinInstitut de Recherche en Communi-cations et Cybernetique de Nantes,UMR CNRS 6597, Ecole Centrale deNantes, Universite de
Nantes, Nantes, [email protected]
Giorgio BartoliniDepartment of Electrical andElectronic Engineering(DIEE), University of Cagliari, Piazzad’Armi, 09123, Cagliari (Italy)[email protected]
Simon BaevElectrical and Computer EngineeringDept., The University of Alabamain Huntsville, 301 Sparkman Dr.,Huntsville, AL, [email protected]
Igor BoikoDepartment of Electrical and Com-puter Engineering, University ofCalgary, 2500 University Dr. N.W.,Calgary, Alberta, [email protected]
Keith BurnhamControl Theory and Applica-tions Centre, Coventry Univer-sity, Coventry CV1 5FB, UK,[email protected]
XVIII List of Contributors
Jose M. CanedoCentro de Investigacion y de EstudiosAvanzados del IPN,A. P. 31-438,C.P. 44550, Guadalajara,Jal., [email protected]
Isaac ChairezDepartment of Automatic ControlCINVESTAV-IPN, AP. 14740, Av.Instituto Politecnico Nacional No.2508, C.P. 07360, Mexico D.F.,[email protected]
Weitian ChenSchool of Engineering Science, SimonFraser University, 8888 UniversityDrive, Vancouver, British ColumbiaV5A 1S6 [email protected]
Jorge DavilaDepartment of Control, EngineeringFaculty, National Autonomous Uni-versity of Mexico (UNAM), 04510,Mexico, D.F., [email protected]
Christopher EdwardsControl and InstrumentationResearch Group, University ofLeicester, Leicester, LE1 7RH, [email protected]
Vicente Feliu BattleEscuela Tecnica Superior de Inge-nieros Industriales, Universidad deCastilla La Mancha, Av. Camilo JoseCela S/N,13005 Ciudad Real, [email protected]
Antonella FerraraDepartment of Computer Engineeringand Systems Science, University of
Pavia, Via Ferrara 1, 27100 Pavia,[email protected]
Thierry FloquetLAGIS UMR CNRS 8146, Ecole Cen-trale de Lille, BP 48, Cite Scientifique,59651 Villeneuve-d’Ascq, [email protected]
Leonid FridmanDepartment of Control, EngineeringFaculty, National Autonomous Uni-versity of Mexico (UNAM), 04510,Mexico, D.F., [email protected]
Katsuhisa FurutaDepartment of Computers andSystems Engineering, Tokyo DenkiUniversity, Hiki-gun, Saitama350-0394, [email protected]
Zbigniew GaliasDepartment of Electrical Engineering,AGH University of Science andTechnology, Krakow, [email protected]
Luisa GiacominiEutecne Srl, Via Galata, 39/8 16121 -Genova, Italy. [email protected]
Parisa KavehElectrical and Computer EngineeringDept., The University of Alabamain Huntsville, 301 Sparkman Dr.,Huntsville, AL, [email protected]
Ali J KoshkoueiControl Theory and Applica-tions Centre, Coventry Univer-sity, Coventry CV1 5FB, UK,[email protected]
List of Contributors XIX
Vincent LebastardInstitut de Recherche en Communi-cations et Cybernetique de Nantes,UMR CNRS 6597, Ecole Centrale deNantes, Universite deNantes, Nantes, [email protected]
Arie LevantApplied Mathematics Department,Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, [email protected]
Alexander G. LoukianovCentro de Investigacion y de EstudiosAvanzados del IPN,A. P. 31-438,C.P. 44550, Guadalajara,[email protected]
Yuri OrlovCICESE Research Center, P.O. BOX434944, San Diego, CA, 92143-4944,[email protected]
Adan OrtizCICESE Research Center, P.O. BOX434944, San Diego, CA, 92143-4944,[email protected]
Mustapha OuladsineLaboratory of sciences of informationsand of systems, SIS UMR 6168 Uni-versity of Paul Cezanne, Aix-MarseilleIII, Avescadrille de Normandie Niemen13397 Marseille Cedex [email protected]
Alessandro PisanoDepartment of Electrical and Elec-tronic Engineering (DIEE), Universityof Cagliari, Piazza d’Armi, 09123,Cagliari (Italy)[email protected]
Yaodong PanThe 21st COE Century Project Office,Tokyo Denki University, Ishisaka, Ha-toyama, Hiki-gun, Saitama 350-0394,[email protected]
Franck PlestanInstitut de Recherche en Communi-cations et Cybernetique de Nantes,UMR CNRS 6597, Ecole Centrale deNantes, Universite deNantes, Nantes, [email protected]
Alexander PoznyakDepartment of Automatic ControlCINVESTAV-IPN, AP. 14740, Av.Instituto Politecnico Nacional No.2508, C.P. 07360, MexicoD.F., [email protected]
Tatyana PoznyakSuperior School of Chemical Engi-neering and Extractive Industries(ESIQIE-IPN), Edif. 7, UPALM, C.P.07738, Mxico, D.F, [email protected]
Elisabetta PuntaInstitute of Intelligent Systems forAutomation, National ResearchCouncil of Italy (ISSIA-CNR), Via DeMarini, 6 - 16149Genoa, [email protected]
Mehrdad SaifSchool of Engineering Science, SimonFraser University, 8888 UniversityDrive, Vancouver, British ColumbiaV5A 1S6 [email protected]
XX List of Contributors
Hebertt Sira RamırezCinvestav IPN, Av. IPN No. 2508,Departamento de Ingenierıa Electrica,Seccion de Mecatronica. ColoniaResidencial Zacatenco AP 14740,07300 Mexico D.F., [email protected]
Ilia ShkolnikovZ/I Imaging Corporation, an Inter-graph Company, 230 Business ParkBlvd., Madison, AL [email protected]
Hassan ShraimLaboratory of sciences of informationsand of systems, SIS UMR 6168 Uni-versity of Paul Cezanne, Aix-MarseilleIII, Avescadrille de Normandie Niemen13397 Marseille Cedex [email protected]
Yuri B. ShtesselElectrical and Computer EngineeringDept., The University of Alabamain Huntsville, 301 Sparkman Dr.,Huntsville, AL, [email protected]
Edgar SanchezCentro de Investigacion y de EstudiosAvanzados del IPN, A. P. 31-438,C.P.44550, Guadalajara, Jal., [email protected]
Adolfo Soto-CotaInstituto Tecnologico de Sonora, 5 deFebrero 818 sur, Cd. Obregon, [email protected]
Sarah SpurgeonControl and Instrumentation ResearchGroup, University of Leicester, Leices-ter, LE1 7RH, UK [email protected]
Elio UsaiDepartment of Electrical and Elec-tronic Engineering (DIEE), Universityof Cagliari, Piazza d’Armi, 09123,Cagliari (Italy)[email protected]
Claudio VecchioDepartment of Computer Engineeringand Systems Science, University ofPavia, Via Ferrara 1, 27100 Pavia,[email protected]
Qing WuSchool of Engineering Science, SimonFraser University, 8888 UniversityDrive, Vancouver, British ColumbiaV5A 1S6 [email protected]
Jian-Xin XuDepartment of Electrical andComputer Engineering, NationalUniversity of Singapore, 4 EngineeringDrive 3, Singapore [email protected]
Xinghuo YuPlatform Technologies Institute,RMIT University, Melbourne, VIC3001, Australia [email protected]
Alan ZinoberDepartment of Applied Math-ematics, The University ofSheffield, Sheffield S10 2TN,UK, [email protected]
Tullio ZolezziDepartment of Mathematics,University of Genoa, Via Dode-caneso, 35 - 16146 Genoa, [email protected]