TNK,

For the answer that relates to \( X(k+1)=\Phi X(k)+\Gamma u(k)\),\(y=CX(k)\)what is the correct way then to plot this so the changes of "T" can be seen.

Is there any other formulas I need or do i just substitute in a value for T then plot.

 

You assume a suitable value for T. Say 0.1 sec ...

Then calculate the \(\Phi\) & \(\Gamma\) matrices

Assume initial value for X(0) and U(0) based on input type [e.g unit step] and go from there with progressive iteration.

\(X(T)=\Phi X(0)+\Gamma U(0)\)
\(Y(T)=C X(T)\)

\(X(2T)=\Phi X(T)+\Gamma U(T)\)
\(Y(2T)=C X(2T)\)

and so on ...

I'd let

\(X(0)=\left[\stackrel{0}{0}\right]\)