Taming Heterogeneity and Complexity of Embedded Control

About Stability Analysis for Discrete Time Systems with Time Varying Delays

 

Laurentiu Hetel – Jamal Daafouz – Claude Iung

Institut National Polytechnique de Lorraine, CRAN UMR 7039 CNRS - UHP - INPL, ENSEM, 2, av. forêt de la Haye, 54516, Vandoevre-Lès-Nancy, Cedex, France. Corresponding author: [e-mail] Work (partially) done in the framework of the HYCON Network of Excellence, contract number FP6-IST-511368

ABSTRACT. This paper is dedicated to the stability analysis for discrete time systems with time varying delay in the state. Two methods are presented and compared. The first one is an extension to discrete time systems of the classical Krasovskii-Lyapunov approach used for continuous-time systems with delays. The second one is based on a switched system transformation approach. The paper aims to establish a theoretical link between the two approaches.

KEYWORDS: time varying delays, discrete time linear systems, switched system, LMI, Krasovskii

– Lyapunov functions

1. Introduction

In this paper the stability analysis for discrete-time linear systems with time varying delays will be considered. Over the past few years, a lot of attention has been paid to the stability of time delay systems. This problem is very challenging when dealing with time varying delays. For continuous time systems with time varying delays stability conditions can be expressed in terms of linear matrix inequalities (LMIs) by using Krasovskii-Lyapunov functionals [RIC ...