Robust Exponential Converge Controller Design for a Unified Chaotic System with Structured Uncertainties via LMI

Neng-Sheng Pai,Her-Terng Yau

doi:10.1155/2010/948590

Abstract

This paper focuses on the chaos control problem of the unified chaotic systems with structured uncertainties. Applying Schur-complement and some matrix manipulation techniques, the controlled uncertain unified chaotic system is then transformed into the linear matrix inequality (LMI) form. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to enforce the prespecified exponential decay dynamics of the uncertain unified chaotic system. Numerical results validate the effectiveness of the proposed robust control scheme.

Highlights

Chaotic behavior of physical systems has been studied since 1963 when the Lorenz system was first introduced 1
The Lorenz system is often taken as a paradigm for demonstrating the effectiveness of control design techniques, since it captures many of the features of chaotic dynamics
The Chen and Ueta 3 and Luand Chen 4 systems, which are derived from Lorenz system, are other popular paradigms

Summary

Introduction

Chaotic behavior of physical systems has been studied since 1963 when the Lorenz system was first introduced 1. An increasing number of studies have formulated the problem of obtaining the Lyapunov-based quadratic stability of uncertain systems as a linear matrix inequality LMI optimization problem 15, lately. Based on the Lyapunov stability criterion, the problem of achieving the robust exponential stability of the uncertain system has first been formulated as an LMI feasible problem. The controller required to achieve a robust exponential stability of the uncertain system has been formulated as a second LMI feasible problem. In 2009, Kuntanapreeda 14 presents an alternative synchronization design for the unified chaotic systems based on Lyapunov stability theory and LMI formulation, when the system uncertainty is not considered. We will take the time-varying perturbation of parameters into account for the robust chaos suppression control problem of uncertain unified chaotic systems in this paper, just by a simple structure linear feedback controller.

System Formulation

Robust Controller Design

Numerical Simulations

Conclusion