Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

Abstract EN

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.