A unified approach to controlling chaos via an LMI-based fuzzy control system design

Abstract

This paper presents a unified approach to controlling chaos via a fuzzy control system design based on linear matrix inequalities (LMI's). First, Takagi-Sugeno fuzzy models and some stability results are recalled. To design fuzzy controllers, chaotic systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to determine structures of fuzzy controllers from the Takagi-Sugeno fuzzy models, LMI-based design problems are defined and employed to find feedback gains of fuzzy controllers satisfying stability, decay rate, and constraints on control input and output of fuzzy control systems. Stabilization, synchronization, and chaotic model following control for chaotic systems are realized via the unified approach based on LMIs. An exact linearization (EL) technique is presented as a main result in the stabilization. The EL technique also plays an important role in the synchronization and the chaotic model following control. Two cases are considered in the synchronization. One is the feasible case of the EL problem. The other is the infeasible case of the EL problem. Furthermore, the chaotic model following control problem, which is more difficult than the synchronization problem, is discussed using the EL technique. Simulation results show the utility of the unified design approach based on LMIs proposed in this paper.