Improved Robust Du-stability measures via S-procedure

In this paper we focus on the notion of robust matrix root-clustering analysis in a union of regions that are possibly disjoint and non symmetric. Indeed this work aims at computing a bound on the size of the uncertainty domain preserving matrix Du-stability. A Linear Fractional Transform (LFT) uncertainty is considered. To reduce conservatism, a new approach, based on some generalized S-procedure, is addressed. In the case where the studied matrices depend affinely on the uncertain parameters or when the studied matrices are subject to polytopic uncertainty, it is known that recently developed L MI conditions are effective to assess the robust performance in a less conservative fashion. This paper further extends the preceding results and propose a unified way to obtain new L MI conditions even in the case of rational parameter dependence. Some conservatism induced by some techniques encountered in the literature is here reduced .