Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

Abstract

This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI) interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D) chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

Synchronization of Discrete-Time Chaotic Fuzzy Systems by means of Fuzzy Output Regulation Using Genetic Algorithm

“…Fuzzy logic and chaos had been considered by many researches and engineers as fundamental concepts and theories and their broad applicability in technology as well. The interaction between fuzzy logic and chaos has been developed for the last 20 years leading to research topics as fuzzy modeling of chaotic systems using Takagi-Sugeno models, linguistic descriptions of chaotic systems, fuzzy control of chaos, synchronization, and a combination of fuzzy chaos for engineering applications [1,2].…”