Chapter 5, Problem 41P

To determine

To prove: The system given can be represented as,

  $\left[\begin{array}{c}{\dot{x}}_1\\ \cdots \\ {\dot{x}}_2\end{array}\right]=\left[\begin{array}{ccc}{A}_1& ⋮& 0\\ \cdots & \cdots & \cdots \\ 0& ⋮& A_2\end{array}\right]\left[\begin{array}{c}{x}_1\\ \cdots \\ x_2\end{array}\right]+\left[\begin{array}{c}{B}_1\\ \cdots \\ B_2\end{array}\right]r;y=\left[\begin{array}{ccc}{C}_1& ⋮& C_2\end{array}\right]\left[\begin{array}{c}{x}_1\\ \cdots \\ x_2\end{array}\right]$ .