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The necessary condition for the stability of the linear system is that all the coefficients of characteristic equation 1+G(s)H(s) =0, be real and have the :

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The necessary condition for the stability of the linear system is that all the coefficients of characteristic equation 1+G(s)H(s) =0, be real and have the :

(a) Positive sign

(b) Negative sign

(c) Same sign

(d) Both positive and negative

I have been asked this question in an online interview.

My question is from Routh-Hurwitz Stability Criterion topic in chapter Stability and Algebraic Criteria of Control Systems

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Correct option is (c) Same sign

For explanation: The necessary condition for the stability of the linear system is that all the coefficients of characteristic equation 1+G(s)H(s) =0, is they must have same sign.

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