Question: A linear second-order continuous time system is described by the following set of differential equations. [ begin{aligned} dot{x}_{1}(t) & =-2 x_{1}(t)+4 x_{2}(t) dot{x}_{2}(t) &
A linear second-order continuous time system is described by the following set of differential equations.
\[
\begin{aligned}
\dot{x}_{1}(t) & =-2 x_{1}(t)+4 x_{2}(t) \\
\dot{x}_{2}(t) & =-2 x_{1}(t)-x_{2}(t)+u(t)
\end{aligned}
\]
where \(x_{1}(t)\) and \(x_{2}(t)\) are the state variables and \(u(t)\) is the control variable. The system is
(a) controllable and stable
(b) controllable and unstable
(c) uncontrollable and unstable
(d) uncontrollable and stable
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