9. For each of the following transfer functions below, state whether the natural response
of the system is stable, unstable, marginally stable, or cannot be determined by
inspection alone. Give a short justification for each answer as below (50pts: 5 per each).
(Bonus: each correct answer will give an extra credit of 5pts) if cannot be determined
by inspection only, use the Routh Methods to determine the stability and locations of
poles in the complex plane.
Transfer function
$\frac{1}{s+1}$
$\frac{-s^2 + 2}{(s^2 + 1)(s^2 + 2)}$
$\frac{6}{s(s + 2)(s + 4)}$
$\frac{25}{s^2(s + 25)}$
$\frac{s^2 - 3s + 5}{(s + 1)(s^2 - 6s + 5)}$
$\frac{2}{(s + 2)(s + 4)(s + 6)}$
$\frac{(s^2 + s + 3)(s^2 + 5s + 7)}{}$
$\frac{1}{2s^4 + s^3 + 13s^2 + s + 20}$
$\frac{1}{2s^4 + s^3 + 13s^2 - s + 20}$
$\frac{81}{(s^2 + 9)^2}$
$\frac{s + 5}{(-s - 2)(s^2 + 2s + 10)}$
$\frac{-s + 4}{s^2 - 4}$
Stability assessment and justification
Stable. First order denominator with positive coefficients.
