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Question

The characteristic polynomial of a system is q(s)=2s5+s4+4s3+2s2+2s+1. The system is

A
stable
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B
marginally stable
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C
unstable
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D
oscillatory
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Solution

The correct option is C unstable
Routh table is
s5242s4121s3000s2s1s0
dds(s4+2s2+1)=0

4s3+4s=0

s=±j,s=±j

dds(s2+1)=0

2s=0

s=0

Double roots on imaginary axis so system is unstable

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