Question

Consider the system \dot{\mathbf{x}}(t)=\left[\begin{array}{rr}

-1 & 0 \\

0 & 0

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

1 \\

0

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

1 & 1

\end{array}\right] x(t) Not all the eigenvalues have negative real parts, but the system is totally stable. How can we explain this?

Fig: 1

Fig: 2

Fig: 3

Fig: 4