ILMI Approach to Static Output Feedback Fuzzy Control for Synchronization of Hyperchaotic Systems via T-S Models

Abstract

A static output feedback fuzzy (SOFF) control approach is proposed in order to deal with the problem of syn- chronization of two identical hyperchaotic systems. The T-S fuzzy model with its small number of fuzzy IF-THEN rules is employed to represent many typical nonlinear hyperchaotic systems. Based on the T-S fuzzy hyperchaotic models and Lyapunov stability theory, a necessary condition for the existence of robust SOFF controllers is presented in terms of a set of matrix inequalities, which guarantees the stable synchronization of two different hyperchaotic systems. An iterative lin- ear matrix inequality (ILMI) algorithm is proposed to compute the feedback gains of the suboptimal SOFF controller. Fi- nally, numerical examples are given to demonstrate the validity and effectiveness of the proposed fuzzy modeling and synchronization scheme of the hyper chaotic systems.