Chapter 5, Problem 5.19P

Given the following state-variable models, obtain the expressions for the matrices A, B, C, and D for the given inputs and outputs.

1. The outputs are $x_1$ and $x_2$ ; the input is u.

$\begin{array}{l}{\stackrel{\dot{}}{x}}_1=-5x_1+3x_2\\ {\stackrel{\dot{}}{x}}_2=x_1-4x_2+5u_2\end{array}$

The output is $x_1$ ; the inputs are $u_1$ and $u_2$ .

$\begin{array}{l}{\stackrel{\dot{}}{x}}_1=-5x_1+3x_2+4u_1\\ {\stackrel{\dot{}}{x}}_2=x_1-4x_2+5u_2\end{array}$