Question

It is known that the dynamic system \dot{\mathbf{x}}(t)=\left[\begin{array}{lll}

\lambda & 1 & 0 \\

0 & \lambda & 0 \\

0 & 0 & \lambda

\end{array}\right] \mathbf{x}(t)+\left[\begin{array}{ll}

1 & 1 \\

0 & 1 \\

1 & 0

\end{array}\right] \mathbf{u}(t) \mathbf{y}(t)=\left[\begin{array}{ccc}

1 & 1 & 0 \\

0 & -1 & 1

\end{array}\right] \mathbf{x}(t) is BIBO stable. Can we conclude that the real-part of is negative? Is the system asymptotically stable?

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