Dissipative Delay-Feedback Control for Nonlinear Stochastic Systems with Time-Varying Delay

Guici Chen,Yongchuan Zhang,Jianzhong Zhou

doi:10.1155/2014/249860

Abstract

The dissipative delay-feedback control problems for nonlinear stochastic delay systems (NSDSs) based on dissipativity analysis are studied in this paper. Based on the Lyapunov stability theory and stochastic analysis technique, both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequalities- (LMIs-) based feasibility tests. The obtained results in this paper for the nominal systems include the available results onH∞approach and passivity for stochastic delay systems as special cases. The delay-dependent feedback controller is designed by considering the relationship among the time-varying delay, its lower and upper bound, and its differential without ignoring any terms, which effectively reduces the conservative. A numerical example is given to illustrate the theoretical developments.

Highlights

The stochastic differential systems appear as a natural description of many observed phenomena of real world, which have been come to play an important role in many fields including population dynamics, macroeconomics, chemical reactor control, communication network, image processes, and mobile robot localization
Since the notation of dissipative dynamical system was introduced by Willems [13], dissipative systems have been of particular interest to researchers in areas of systems, circuits, networks and control, and so forth
The systems are subjected to stochastic disturbance, nonlinear disturbance, and two cases time-delay effects, which often exist in a wide variety of industrial processes and are the main sources of instability

Summary

Introduction

The stochastic differential systems appear as a natural description of many observed phenomena of real world, which have been come to play an important role in many fields including population dynamics, macroeconomics, chemical reactor control, communication network, image processes, and mobile robot localization. On the other hand, studying the dissipativity analysis and synthesis problems has a strong motivation due to their simplicity and effectiveness in dealing with robust and nonlinear systems. Among the relevant topics are the dissipativity analysis and synthesis for time-delay systems [16, 17] These results show that the dissipativity-based methods are highly effective in design the robust controller. Dissipative delayfeedback control problems for nonlinear stochastic systems with time-varying delay are studied based on dissipativity. The delay-dependent feedback controller is designed by considering the relationship among the time-varying delay, its lower and upper bound, and its differential without ignoring any terms, which effectively reduces the conservative

Problems Statement and Preliminaries

Dissipativity Analysis for NSDSs

Dissipative Delay-Feedback Control for NSDSs

Numerical Example with Simulation

Conclusions