Question

The Positiveness of the coefficients of characteristic equation is necessary as well as sufficient condition for:

(a) First order system

(b) Second order system

(c) Third order system

(d) None of the mentioned

I had been asked this question during an interview for a job.

I'd like to ask this question from Necessary Conditions for Stability and Non-Linear Systems topic in section Stability and Algebraic Criteria of Control Systems

Answer 1

The correct option is (c) Third order system

To elaborate: It does not ensure the negativeness of the real parts of the complex roots of the third or higher order systems.