zbMATH — the first resource for mathematics

Static output feedback design for uncertain linear discrete time systems. (English) Zbl 1049.93069
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.

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)
Full Text: DOI