Stabilization Criteria for Bilinear Systems with Time-varying Delay

Pin-Lin Liu

doi:10.13189/ujeee.2014.020202

Abstract

In this paper we consider the problem of stabilizing a bilinear system with time- varying delay via linear state feedback control. Based on the Lyapunov method, a delay-dependent criterion for determining the stabilization of system is obtained in terms of linear matrix inequalities (LMIs) and used to express the relationships between the terms in the Leibniz-Newton formula, which can be easily solved by efficient convex optimization algorithms. From the numerical examples, the obtained results have some significant improvements over the recent literatures.

Highlights

The phenomena of time-delay are very often encountered in control systems, economic systems and even population dynamics, etc
Since delay is usually time-varying in many practical systems, many approaches have been developed to derive the delay-dependent stability criteria for systems with time-varying delays
The objective of this paper is to study the problem of stabilization of bilinear systems with time-varying delay by means of state feedback control law

Summary

Introduction

The phenomena of time-delay are very often encountered in control systems, economic systems and even population dynamics, etc. The state feedback control of bilinear systems with time delay has been addressed by means of a linear matrix inequality (LMI)optimization problem in [11, 12], where an estimate of the domain of attraction is computed. The result in [11] gives only stability conditions for the closed-loop bilinear time-delay systems with given controllers, and their given controllers are state feedback controllers. It did not propose even state feedback controller design method. The objective of this paper is to study the problem of stabilization of bilinear systems with time-varying delay by means of state feedback control law. The advantage of the approach is illustrated by numerical examples

Stability Description and Preliminaries

State Feedback Control for Time-Varying Delay Systems

Illustrative Examples

Conclusion