$\frac{Y(s)}{V(s)} = \frac{3s+4}{s^2 +5s +6}$

Mumbai University > Electronics Engineering > Sem 4 > Linear Control Systems

Topic : State Variable Models

Difficulty : High

Marks : 10M

Properties of state Transition matrix =>

1) $\phi(o)$ = $e^{Ao}$ = I

2) $\phi(t) = e^{At} = [\phi(-t)]^{-1}$

i.e. $\phi^{-1}(t) = \phi(-t)$

3) $\phi(t_1 + t_2) = e^{A(t_1+t_2)}$

=$e^{At_1}.e^{At_2} = \phi(t_1).\phi(t_2)$

4) $[\phi(t)]^n = [e^{At}]^n$

= $\phi(nt)$

5) $\phi(t_2-t_1).\phi(t_1-t_o) = \phi(t_2-t_o)$

Given =>

$\frac{Y(s)}{V(s)} = \frac{3s+4}{s^2 + 5s + 6}$ …