Stability robustness computation of quasipolynomials with affine coefficient perturbations

This paper considers the problem of the stability robustness computation of quasipolynomials with coefficients which are affine functions of the parameter perturbations. A quasipolynomial is said to be stable if its roots are contained in an arbitrarily pre-specified open set in the complex plane, and its stability robustness is then measured by the norm of the smallest parameter perturbation which destabilizes the quasipolynomial. 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 ∞-norm, 2-norm or 1-norm