Question

The condition for stability of a closed-loop system with a characteristic $s^3+b{s}^2+cs+1=0$, with positive coefficients is

• A. $b+c>1$
• B. $bc>1$
• C. $b=c$
• D. $b>c$

Answer 1

The correct option is B $bc>1$

For the system to be stable.
By Routh Hurwitz criteria
$\therefore$ for the system to be stable, all the elements of the column 1 should be > 0

$\therefore$ $\frac{bc-1}{1}>0$

$\therefore$ $bc-1>0$

$bc>1$