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 D_u-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 afflnely on the uncertain parameters or when the studied matrices are subject to polytopic uncertainty, it is known that recently developed L.M.J 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.M.J conditions even in the case of rational parameter dependence. Some conservatism induced by some techniques encountered in the literature is here reduced .