$$ x = \begin{bmatrix} 0 & 6 & -5\\ 1 & 0 & 2\\ 3&2&4 \end{bmatrix} \space x + \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \space u $$ $$ y = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \space x$$

Topic : State Variable Models

Difficulty : High

Marks : 10M

Given:

$A=\begin{bmatrix} 0 & 6 & -5 \\ 1 & 0 & 2 \\ 3 & 2 & 4 \end{bmatrix}-----(1)$

$B=\begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}-----(2)$

$C=\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}-----(3)$

Since A is a 3x3 matrix, so n=3.

Controllability: The necessary and sufficient condition for controllability …