Using the Routh-Hurwitz crition, determine if the following systems are stable or unstable, and how many roots lie in th

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Using the Routh-Hurwitz crition, determine if the following
systems are stable or unstable, and how many roots lie in the
left-hand plane of the s-plane diagram. (i) 𝑇(𝑠) = 𝑠 3 + 2𝑠 2 + 6 𝑠
5 + 6𝑠 3 + 5𝑠 2 + 8𝑠 + 20 (ii) 𝑇(𝑠) = 1 2𝑠 2 + 5𝑠 3 + 𝑠 2 + 2𝑠 +
1
(b) For the negative closed loop feedback system with an open
loop gain 𝐺(𝑠) and a feedback gain 𝐻(𝑠) = 1, where 𝐺(𝑠) = 𝐾 (𝑠 − 𝑎)
𝑠(𝑠 + 𝑏) determine the range of values for the gain 𝐾 when (i) 𝑎
< 0 and 𝑏 < 0, and (ii) 𝑎 > 0 and 𝑏 > 0.