The state space equation is given as [ẋ1; ẋ2] = [[-3, 1], [0, -2]] [x1; x2] + [0; 1] U, x1(0) = 0, x2(0) = 0 and [Y] = [-1 1] [x1; x2]. The system is
- A. Controllable and observable
- B. Controllable and not observable
- C. Not controllable and observable
- D. Not controllable and not observable
Answer: B. Controllable and not observable
Explanation: Controllability matrix [B, AB] has rank 2 (controllable), while observability matrix [C; CA] has rank 1 < 2 (not observable).