Question

A. Obtain state space representation of following transfer function in Phase variable canonical form, OCF and CCF by Direct Decomposition of Transfer Function Similarity Transformation \frac{Y(s)}{U(s)} = \frac{s^2 + 2s + 3}{s^3 + 5s^2 + 3s + 2} B. Develop the Kalman decomposition of the following system and write a minimal realization for it. $\dot{x} = \begin{bmatrix} 1 & 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 2 & 0 & 0 \ 0 & 0 & 0 & 3 & 0 \ 0 & 0 & 0 & 0 & 3 \end{bmatrix} x + \begin{bmatrix} 0 \ 1 \ 0 \ 0 \ 1 \end{bmatrix} u$ y = $\begin{bmatrix} 0 & 1 & 1 & 0 & 1 \end{bmatrix} x + u$

          A. Obtain state space representation of following transfer function in Phase
variable canonical form, OCF and CCF by
Direct Decomposition of Transfer Function
Similarity Transformation
\frac{Y(s)}{U(s)} = \frac{s^2 + 2s + 3}{s^3 + 5s^2 + 3s + 2}
B. Develop the Kalman decomposition of the following system and write a
minimal realization for it.
$\dot{x} = \begin{bmatrix} 1 & 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 2 & 0 & 0 \ 0 & 0 & 0 & 3 & 0 \ 0 & 0 & 0 & 0 & 3 \end{bmatrix} x + \begin{bmatrix} 0 \ 1 \ 0 \ 0 \ 1 \end{bmatrix} u$
y = $\begin{bmatrix} 0 & 1 & 1 & 0 & 1 \end{bmatrix} x + u$

A. Obtain state space representation of following transfer function in Phase
variable canonical form, OCF and CCF by
Direct Decomposition of Transfer Function
Similarity Transformation
(Y(s))/(U(s)) = (s^2 + 2s + 3)/(s^3 + 5s^2 + 3s + 2)
B. Develop the Kalman decomposition of the following system and write a
minimal realization for it.
ẋ =
< b m a t r i x >
x +
< b m a t r i x >
u
y = < b m a t r i x >
x + u

Added by Ismael S.

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