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# Stability Theory – 1 – 6

26. If the system has multiple poles on the jω axis, the system is :

(a) stable
(b) unstable
(c) marginally stable
(d) conditionally stable

Explanation
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27. When the system is excited by an unbounded input and produces an unbounded output :

(a) the system is stable
(b) the system is unstable
(c) the system is conditionally stable
(d) nothing can be said about stability

Explanation
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28. The number of sign changes in the elements of the first column of the Routh array denotes :

(a) the number of zeros of the closed-loop system in the RHP
(b) the number of poles of the closed-loop system in the RHP
(c) the number of open-loop zeros in RHP
(d) the number of open-loop poles in RHP

Explanation
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29. The terms in the first column of the Routh array of the characteristic equation of a certain system are 4, 7, 6, -5, -4, -3. The number of roots of the characteristic equation in the right-half of the s-plane is equal to :

(a) 2
(b) 1
(c) 3
(d) none of these

Explanation
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30. The characteristic equation 1 + G(s)H(s) = 0 of a system is given by s4 + 8s3 +12s2 +8s + K = 0 For the system to remain stable, the value of gain K should be :

(a) zero
(b) 0< K
(c) >11
(d) positives