Problem #$4$: $(8$pts$)$

Transfer function of a complex control system is given below.

$T(s)=\frac{30s^3+3s^2+s}{s^5+2s^4+3s^3+6s^2+2s+4}$

a$)$ Observe system's stability according to coefficient tests and mention your findings.

b$)$ Design the Routh array for stability of this system with Routh Hurwitz stability criterion.

c$)$ Mention the number of characteristic roots on all significant locations of $s-$plane.

d$)$ Specify this system as stable, unstable, or marginally stable and mention the reason for your claim.