A SISO system is represented by the state$-$space model $=(1210)()+(10)()()=(1010)()+().$ x $$ y$($t$)=(1120)$x$($t$)+(01)$u$($t$)=(1010)$x$($t$)+$u$($t$).$ Compute the state transition matrix $\backslash$Phi $()=()\backslash$Phi $($t$)=$e At u o $($t$).$ Check your answer by showing that $\backslash$Phi $(0)=\backslash$Phi $(0)=$I. $()$ u o $($t$)$ unit$-$step functionA SISO system is represented by the state$-$space model

$x^{}=([-1,2$

$1,0])x(t)+(\frac{1}{0})u(t)$

$y(t)=([10,-10])x(t)+u(t).$

Compute the state transition matrix $(t)=e^{At}{u}_o(t).$ Check your answer by showing that $(0)=$I.