Robust Matrix Root-Clustering Analysis through Extended KYP Lemma

This paper is dedicated to robust matrix eigenvalue clustering in a subregion ${\mathcal D}$ of the complex plane. A norm-bounded uncertainty is considered. $\cD$ is any intersection and/or union of half planes, discs, and outsides of discs. This work aims at computing the associated complex $\cD$-stability radius. This challenge was already tackled in a recent paper but the technique therein may fail or lead to conservative results when the subregions overlap. The present paper proposes to circumvent those limits thanks to an extended version of the Kalman-Yakubovich-Popov (KYP) lemma which is deduced from the so-called generalized S-procedure.