Consider a linear system whose state space representation is $\dot{x}\left(t\right)=Ax\left(t\right).$If the initial state vector of the system is $x\left(0\right)=\left[\begin{array}{c}1\\ -2\end{array}\right]$,then the system response is $x\left(t\right)=\left[\begin{array}{c}{e}^{-2t}\\ -2e^{-2t}\end{array}\right].$ If the initial state vector of the system changes to $x\left(0\right)=\left[\begin{array}{c}1\\ -1\end{array}\right],$ then the system response becomes $x\left(t\right)=\left[\begin{array}{c}{e}^{-t}\\ -e^{-t}\end{array}\right].$



The eigen-value and eigen-vector pairs $({\lambda }_i,v_i)$ for the system are

Other Control Systems . 6 months ago

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