GATE 2014 EC (EC4) – Question 57
$G_p(s)=(ps^2+3ps-2)/[s^2+(3+p)s+(2-p)]$, with p positive real. Find the maximum value of p until which G_p remains stable.
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Correct answer: 1.9 to 2.1
Explanation
The denominator is s²+(3+p)s+(2−p). For a second-order polynomial, strict Hurwitz stability requires both coefficients positive. With p>0the first is positive, while2−p>0requires p<2. Thus **2** is the upper boundary or supremum of the stability interval starting at positive small p; at p=2a pole reaches zero, so the endpoint is not strictly stable. Isolated exact pole-zero cancellations are not robust internal stability.