A Criterion for Hurwitz Polynomials and its Applications

We present a new criterion to determine the stability of polynomial with real coefficients. Combing with the existing results of the real and negative roots discrimination, we deduced the explicit conditions of stability for any real polynomial with a degree no more than four. Meanwhile, we discussed the problem of controls system stability and inertia of Bezout matrix as the applications of the criterion. A necessary and sufficient condition to determine the stability of the characteristic polynomial of the continuous time control systems was proposed. And also, we discussed a pathological case of the bilinear transformation, which can convert the stability analysis of a given discrete time system to the corresponding continuous time system, and brought forward an alternative one.