Robust root-clustering analysis in a union of subregions

This paper addresses the research of robustness bounds for systems described by linear state space models. These bounds on the norm of unstructured uncertainties guarantee that the eigenvalues of the perturbed state matrix remain in a region of the complex plane in which the eigenvalues of the nominal state matrix lie. The bounds are obtained through a linear matrix inequalities (LMI) approach. This allows to choose not only some special simple convex region, (symmetric with respect to the real axis since the state matrix is real), but also some special non-convex (but symmetric) union of convex subregions, each of them being not necessarily symmetric with respect to the real axis. It can be of interest in the problems of robust design where one wants to specify different regions for dominant and not dominant pole-clustering. This larger choice of regions in the computation of such robustness bounds is an original aspect of the the presented work.