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

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Topic : State Variable Models

Difficulty : High

Marks : 5M or 10M

Controllability

$\dot{x(k)}$ = A x(k) + B u(k) ---(1)

y(k) = C x(k) + D u(k)

The necessary and sufficient condition for controllability is that rank of the composite matrix Qc is n,

Qo = [B: AB : $A^2B$ : ---------$A^{n-1}B$]

Defination : The equation (1) is said to be …