Question

2 (15) Indicate whether the following are true or false:

(a) Every minimal realization of a SISO system is controllable.

(b) Every minimal realizationof a SISO system is observable.

(c) Every minimal realization of a SISO system has a coprime rational transfer function.

(d) A realization with coprime rational transfer function must be controllable and observable.

(e) Every realizable system can be reduced to a form that is controllable and observable.

(f) Every system with a proper rational transfer function is realizable.

(g) Every asymptotically stable system is marginally stable.

(h) Every marginally stable system is asymptotically stable.

(i) Every realizable system is asymptotically stable.

(j) Every realizable system is marginally stable.

(k) If a system is controllable it must be asymptotically stable.

(l) If a system is observable and controllable, it must be asymptotically stable.

(m) If two systems are zero-state equivalent, they must be equivalent.

(n) If a linear time-invariant system is BIBO stable, it must be internally stable.

(o) If a minimal linear time-invariant system is BIBO stable, it must be internally stable.

Answer 1

1. True

2. False (controllable but not observable)

3. True

4. True

5. False. Some systems can be neither controllable nor observable.

6. True. It can be realized whether the system is controllable or observable or not.

7. False. It can be unstable too.

8. True . As asymptotes meet Imaginary axis at infinity.

9. False. It can be either stable or unstable also.

10. False. It can be either stable or unstable or marginally stable.

11. False.

12. False.

13. True.

14. True.

15. True.