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Question 13.3: Determine the stability of a system that has the characteris...

Determine the stability of a system that has the characteristic equation

s^{3} +2s^{2}+4s+9=0.

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The Routh array is

\begin{matrix} s^{3} \\ s^{2} \\ s^{1} \\ s^{0} \end{matrix}\Biggm| \begin{matrix} 1 & 4 \\ 2 & 9 \\ -0.5 & \\9 & \end{matrix}

The system is unstable and there are two roots in the right half of the complex plane, as indicated by two sign changes in the first column of the Routh array, from 2 to −0.5 and from −0.5 to 9.

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