Stability of perturbed polynomials based on the argument principle and nyquist criterion

The stability robustness of the characteristic polynomial with perturbed coefficients for linear time-invariant systems is studied. The Schur, strictly Hurwitz, and Gstability properties of perturbed polynomials are all considered with a unified approach. New upper bounds on the allowable coefficient perturbation of a polynomial, for keeping one of the stability properties, are obtained. The proposed upper bounds are directly formulated in terms of the polynomial coefficients and can be computed easily.Wealso provide a sufficient condition for the discrete stability of interval polynomials and an algorithm for testing the G-stabilityof polynomials with constant coefficients. Illustrative examples are given to show the applicability of our results, especially in determining measures of stability robustness for any Schur polynomial subject to coefficient perturbation.