Stability Analysis of Linear Discrete-Time Systems with Interval Delay: A Delay-Partitioning Approach

Priyanka Kokil,V. Krishna Rao Kandanvli,Haranath Kar

doi:10.5402/2011/624127

Abstract

This paper considers the problem of asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By using a delay partitioning-based Lyapunov functional, a new criterion for the asymptotic stability of such systems is proposed in terms of linear matrix inequalities (LMIs). The proposed stability condition depends on both the size of delay and partition size. The presented approach is compared with previously reported approaches.

Highlights

Mathematical models with time delays are frequently encountered in various physical, industrial, and engineering systems due to measurement and computational delays, transmission and transport lags
This paper considers the problem of asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state
Though the approach in 37 provides less conservative results than 22, 29, it would lead to heavier computational burden and more complicated synthesis procedure

Summary

Introduction

Mathematical models with time delays are frequently encountered in various physical, industrial, and engineering systems due to measurement and computational delays, transmission and transport lags. Delay-dependent stability criteria generally lead to less conservative results than delay-independent ones, especially if the size of time delay is small 8–12. Though the approach in 37 provides less conservative results than 22, 29 , it would lead to heavier computational burden and more complicated synthesis procedure. Motivated by these developments, this paper studies the problem of stability analysis of linear discrete-time system with interval-like time-varying delay in the state.

Model Description and Preliminaries

Main Result

Methods

A Numerical Example

Conclusion