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Question 13.4: Determine the range of values of K for which the system havi...

Determine the range of values of K for which the system having the following character-istic equation is stable:
s^{3} +s^{2}+\left(5+K\right)s+3K=0   .

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The Routh array is

\begin{matrix} s^3 \\ s^2 \\ s^1 \\ s^0 \end{matrix} \Biggr| \begin{matrix} 1 & 5+K \\ 1 & 3K \\ 5-2K & \\ 3K & \end{matrix}

There will be no sign changes in the first column of the Routh array if

5-2K\gt 0 and 3K\gt 0,
which give the following range of K for stability:
0\lt K\lt 2.5 .

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