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 synchronization 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 linear matrix inequality (ILMI) algorithm is proposed to compute the feedback gains of the suboptimal SOFF controller. Finally, numerical examples are given to demonstrate the validity and effectiveness of the proposed fuzzy modeling and synchronization scheme of the hyper chaotic systems.

Keywords:

Hyperchaotic systems, iterative linear matrix inequality (ILMI), robust synchronization, static output feedback fuzzy controller, T-S fuzzy Models.