A simple procedure for the exact stability robustness computation of polynomials with affine coefficient perturbations

The authors consider the problem of the stability robustness computation of polynomials with coefficients which are affine functions of the parameter perturbations. A polynomial is said to be stable if its roots are contained in an arbitrary prespecified open set in the complex plane, and its stability robustness is then measured by the norm of the smallest parameter perturbation which destabilizes the polynomial. A simple and numerically effective procedure, which is based on the Hahn-Banach theorem of convex analysis and which is applicable for any arbitrary norm, is obtained to compute the stability robustness. The computation is then further simplified for the case when the norm used is the Holder infinity -norm, 2-norm, or 1-norm.<>