# Stability using Routh Stability Criterion

Determine the stability of the system whose characteristics equation is:

$a(s) = 2s^5 + 3s^4 + 2s^3 + s^2 + 2s + 2$.

# Solution

All coefficients are positive and non-zero; therefore, the necessary condition for stability is satisfied. Let's write the Routh array:

$\begin{array}{l | c c c} s^5 & 2 & 2 & 2 \\ s^4 & 3 & 1 & 2 \\ s^3 & & & \\ s^2 & & & \\ s^1 & & & \\ s^0 & & &\end{array}$