LMI approach to robust stability and stabilization of nonlinear uncertain discrete-time systems with convex polytopic uncertainties

Manlika Rajchakit ,Grienggrai Rajchakit

doi:10.1186/1687-1847-2012-106

Manlika Rajchakit , Grienggrai Rajchakit

Open Access

https://doi.org/10.1186/1687-1847-2012-106

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Journal: Advances in Difference Equations	Publication Date: Jul 16, 2012
Citations: 8	License type: CC BY 2.0

Affiliation: Maejo University

Abstract

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:15A09, 52A10, 74M05, 93D05.

Highlights

1 Introduction Since the time delay is frequently viewed as a source of instability and encountered in various engineering systems such as chemical processes, long transmission lines in pneumatic systems, networked control systems, etc., the study of delay systems has received much attention and various topics have been discussed over the past years
The parameter-dependent Lyapunov-Krasovskii functionals are constructed as the convex combination of a set of functions assures the robust stability of the nominal systems and the stability conditions must be solved upon a grid on the parameter space, which results in testing a finite number of linear matrix inequalities (LMIs) [, ]
Using the parameter-dependent Lyapunov-Krasovskii functional combined with LMI techniques, we propose new criteria for the robust stability of the nonlinear uncertain system

Summary

Introduction

Since the time delay is frequently viewed as a source of instability and encountered in various engineering systems such as chemical processes, long transmission lines in pneumatic systems, networked control systems, etc., the study of delay systems has received much attention and various topics have been discussed over the past years. A number research works for dealing with asymptotic stability problem for discrete systems with interval time-varying delays have been presented in [ – ]. Stability analysis of the systems with time-varying delays is more complicated, especially for the case where the system matrices belong to some convex polytope.

Results

Conclusion