(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the transfer function [tex] H(s)=\cfrac{1}{a_{2}s^{2}+a_{1}s+a_{0}} [/tex]

where real-valued coefficients [itex]a_{2},a_{1}, a_{0}[/itex] are arbitrary except that [itex]a_{2}[/itex] is nonzero. Verify that the system is stable iff the coefficients [itex]a_{2},a_{1}, a_{0}[/itex] have the same sign.

2. Relevant equations

Professor gave us a hint to observe the quadratic formula

3. The attempt at a solution

I really don't know how to start it. I've tried a prove by cases but got bogged down fairly quickly. I can post what I have if this is the correct approach but I have doubts that it is. I just kept gaining more and more cases. A couple of hints towards the right direction would be most helpful

EDIT: I should note that I understand that for the system to be stable all the poles (2 in this case) of the transfer function should be in the LHP. That is that the the Re(p)<0 where p is the pole.

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# Homework Help: Conditions of Stability for second order system

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