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

Mehdi, D.; Boukas, E. K.; Bachelier, O.

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)

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