Multiple choice

Consider the state space model of a system, as given below:

$\begin{bmatrix} \ . \ \ x_1 \ \ . \ \ x_2 \ \ . \ \ x_3 \ \end{bmatrix}$ = $\begin{bmatrix} \ -1 & 1 & 0 \ \ 0 & -1 & 0 \ \ 0 & 0 &-2 \ \end{bmatrix}$$\begin{bmatrix} \ x_1 \ \ x_2 \ \ x_3 \ \end{bmatrix}$ + $\begin{bmatrix} \ 0 \ \ 4 \ \ 0 \ \end{bmatrix}$ u; y = $\begin{bmatrix} \ 1 & 1 & 1\ \end{bmatrix}$$\begin{bmatrix} \ x_1 \ \ x_2 \ \ x_3 \ \end{bmatrix}$

The system is

  1. controllable and observable

  2. uncontrollable and observable

  3. uncontrollable and unobservable

  4. controllable and unobservable
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Therefore, the rank of observability matrix is Rank($O_M$) = 3 = order of system. Hence, the system is observable.

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