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GATE ECE 1991 | Question-12

A linear second order single input continuous time system is described by the following set of differential equations

$$ \begin{aligned} &x_1(t)=-2 x_1(t)+4 x_2(t) \\ &x_2(t)=2 x_1(t)-x_2(t)+u(t) \end{aligned} $$

Where $x_1(t)$ and $x_2(t)$ are the state variables and $u(t)$ is the control variable. The system is:

  1. controllable and stable
  2. controllable but unstable
  3. uncontrollable and unstable
  4. uncontrollable and stable
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