Fuzzy Modeling and H¥ Synchronization of Different Hyperchaotic Systems via T–S Models

Abstract

In this paper, a unified fuzzy H¥ control approach is proposed to deal with the problem of synchronization of two different hyperchaotic systems. The T-S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. Based on the T-S fuzzy hyperchaotic models, a fuzzy H¥ synchronization controller is designed via parallel distributed compensation (PDC) techniques. The sufficient condition for the H¥ synchronization of two different hyperchaotic systems is derived by applying Lyapunov stability theory. The results are expressed in terms of LMIs, and therefore it is very convenient to check in practice. This method is a universal one for synchronization of two different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy modeling and hyperchaotic synchronization scheme.