Delay-Dependent Guaranteed Cost Control of an Interval System with Interval Time-Varying Delay

Min Xiao,Zhongke Shi

doi:10.1155/2009/360928

Abstract

This paper concerns the problem of the delay-dependent robust stability and guaranteed cost control for an interval system with time-varying delay. The interval system with matrix factorization is provided and leads to less conservative conclusions than solving a square root. The time-varying delay is assumed to belong to an interval and the derivative of the interval time-varying delay is not a restriction, which allows a fast time-varying delay; also its applicability is broad. Based on the Lyapunov-Ktasovskii approach, a delay-dependent criterion for the existence of a state feedback controller, which guarantees the closed-loop system stability, the upper bound of cost function, and disturbance attenuation lever for all admissible uncertainties as well as out perturbation, is proposed in terms of linear matrix inequalities (LMIs). The criterion is derived by free weighting matrices that can reduce the conservatism. The effectiveness has been verified in a number example and the compute results are presented to validate the proposed design method.

Highlights

Stability analysis, and control synthesis of the uncertainty interval systems and the time-delay system have been discussed extensively 1–7
We present a new method of dealing with the problem of the delaydependent stability and guaranteed cost H∞ control of interval system with interval timevarying delay based on the LMIs 25
The following theorem presents a sufficient condition for the existence of the nonfragile guaranteed cost controller

Summary

Introduction

Stability analysis, and control synthesis of the uncertainty interval systems and the time-delay system have been discussed extensively 1–7. The guaranteed cost-control approach aims at stabilizing the systems while maintaining an adequate level. Fragility is a common dynamic problem and is caused by many factors; reduction in size and cost of digital control hardware results in limitations in available computer memory and word length capabilities of the digital processor 11–15. Literature 7 studies the guaranteed cost control of the interval system but does not consider the time delay and the fragility or the results presented by the proposed M− matrix conditions. Very little open literature covering the research guaranteed cost control of an interval system with time delay has been published and the fragility problem has not been considered

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Conclusion