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LMI approach to robust stability and stabilization of nonlinear uncertain discrete-time systems with convex polytopic uncertainties. (English) Zbl 1346.93312

Summary: This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results.

MSC:

93D09 Robust stability
15A09 Theory of matrix inversion and generalized inverses
52A10 Convex sets in \(2\) dimensions (including convex curves)
74M05 Control, switches and devices (“smart materials”) in solid mechanics
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