A control system is described by the following state model
\(\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{r}} { - 1}&0\\ 0&{ 3} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 1\\ 1 \end{array}} \right]U\left( t \right)\;\)
\(y\left( t \right) = \left[ {\begin{array}{*{20}{c}} 1&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right] \)
The system is:
1
controllable and observable
2
controllable but not observable
3
stable
4
unstable