Without using the Routh-Hurwitz criterion, determine if the following systems are asymptotically stable, marginally stable, or unstable.

Question:

Without using the Routh-Hurwitz criterion, determine if the following systems are asymptotically stable, marginally stable, or unstable. In each case, the closed-loop transfer function is given.

(a)

\[M(s)=\frac{10(s+2)}{s^{3}+3 s^{2}+5 s}\]

(b)

\[M(s)=\frac{K}{s^{3}+5 s+5}\]

(c)

\[M(s)=\frac{100}{s^{3}-2 s^{2}+3 s+10}\]

(d)

\[M(s)=\frac{s-1}{(s+5)\left(s^{2}+2ight)}\]

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