engineering recuitment GATE ECE 2023-24 Test Series Control Systems State Space Analysis Solution To the State Equation
Given the homogenous state-space equation \(\dot x = \left[ {\begin{array}{*{20}{c}} { - 3}&1\\ 0&{ - 2} \end{array}} \right]x\). The steady-state value of \({x_{ss}} = \mathop {\lim }\limits_{t \to \infty } x\left( t \right)\), given the initial state value of x(0) = [10 - 10]T is
1
\({x_{ss}} = \left[ {\begin{array}{*{20}{c}} 0\\ 0 \end{array}} \right]\)
2
\({x_{ss}} = \left[ {\begin{array}{*{20}{c}} { - 3}\\ { - 2} \end{array}} \right]\)
3
\({x_{ss}} = \left[ {\begin{array}{*{20}{c}} { - 10}\\ {10} \end{array}} \right]\)
4
\({x_{ss}} = \left[ {\begin{array}{*{20}{c}} \infty \\ \infty \end{array}} \right]\)