Question

The characteristic polynomial of a system is $q\left(s\right)=2s^5+s^4+4s^3+2s^2+2s+1.$ The system is

• A. stable
• B. marginally stable
• C. unstable
• D. oscillatory

Answer 1

The correct option is C unstable

Routh table is
$\begin{array}{cccc}{s}^5& 2& 4& 2\\ s^4& 1& 2& 1\\ s^3& 0& 0& 0\\ s^2& & & \\ s^1& & & \\ s^0& & & \end{array}$
$\therefore \frac{d}{ds}(s^4+2s^2+1)=0$

$\Rightarrow 4s^3+4s=0$

$s=\pm j,s=\pm j$

$\frac{d}{ds}(s^2+1)=0$

$\Rightarrow 2s=0$

$\Rightarrow s=0$

Double roots on imaginary axis so system is unstable