Mehdi, D.; Boukas, E. K.; Bachelier, O. Static output feedback design for uncertain linear discrete time systems. (English) Zbl 1049.93069 IMA J. Math. Control Inf. 21, No. 1, 1-13 (2004). The paper focuses on the design of a static output feedback stabilizing a discrete-time linear system affected by polytopic parametric uncertainty. The authors apply verbatim recent results by Peaucelle and Arzelier, originally inspired by previous works by de Oliveira, Bernussou and Geromel, to convert static output feedback stabilization (a difficult open problem in control theory) into a (convex, hence much easier) optimization problem over linear matrix inequalities (LMI). Unsurprisingly, the obtained LMI conditions are only sufficient, hence potentially conservative or pessimistic. The basic idea is to convexify the original non-convex conditions by introducing slack variables in such a way that a stabilizing static output feedback gain may be derived from a stabilizing state feedback gain, the latter being found by solving an LMI problem. Reviewer: Didier Henrion (Toulouse) Cited in 28 Documents MSC: 93D15 Stabilization of systems by feedback 93D09 Robust stability 15A39 Linear inequalities of matrices 93C55 Discrete-time control/observation systems 93B40 Computational methods in systems theory (MSC2010) Keywords:static output feedback stabilization; linear matrix inequalities; convexification; discrete-time linear system; polytopic parametric uncertainty PDF BibTeX XML Cite \textit{D. Mehdi} et al., IMA J. Math. Control Inf. 21, No. 1, 1--13 (2004; Zbl 1049.93069) Full Text: DOI OpenURL