Observer-based control design via LMIs for a class of switched discrete-time linear systems with parameter uncertainties

International audienceThis paper deals with observer-based controller design method via Linear Matrix Inequalities~(LMIs) for a class of switched discrete-time linear systems. The main contribution consists in providing different scenarios of the use of Finsler's Lemma to reduce the conservatism of some previous results in the literature. Thanks to this scenarios and the use of some other new mathematical tools, one of the objectives of this paper is to open new research directions for other control design problems. The validity and effectiveness of the proposed design methodologies are shown through a numerical example