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A feedback system has an open-loop transfer function of \[ G(s) H(s)=\frac{k e^{-s}}{s\left(s^{2}+5 s+9\right)} \] Using Routh criterion, find the maximum value of \( k \) for the closed-loop system to be stable.

solution: step1: G(s)H(s)=ke?ss(s2+5s+9)e?ts=1?