page 6-1 to 6-37

Requirements

1. Controllability Definition.2. Prove part (2) of Theorem 6.1.3. Abilities to determine the controllability using the controllability Gramian Wc(t) and the controllability

matrix.4. Concepts of controllability indices and the controllability index and methods to determine them. Range of

the controllability index and why.

Requirements

5. Observability Definition.6. Prove Theorem 6.4.7. Derive the equation which determine X(0) using the non-singular Wo(t). 8. Abilities to determine the observability using the observability Gramian Wo(t) and the observability

matrix.9. Concepts of observability indices and the observability index and methods to determine them. Range of the

observability index and why. 10. Duality of controllability and observability.

HW for Controllability and Observability:

6.1-6.7

HW: 6.8-6.16, 6.19-6.23(6.1-6.7 have also been assigned)

Requirements: 6.4-6.8

1. Abilities to obtain the controllable and observable canonical forms. Determine transfer function from canonical forms.

2. Proof of Theorem 6.6.3. Kalman decomposition. Determine the transfer function.4. Abilities to determine the controllability and observability for Jordan form equations.5. Determination of the controllability and observability of discrete-time system using A, B, C.6. If is full rank, then is controllable. Prove.7. Relationship of the discredited system with the original continuous-time system in controllability.8. Definitions of the controllability and observability for time-varying systems.9. Theorem 6.11 and its proof.10. Theorem 6.12: prove and use it and its observabilty extension to determine time-varying systems’

controllability and observability