Invariant Ellipsoids Method for Chaos Synchronization in a Class of Chaotic Systems

This paper presents an invariant sets approach for chaos synchronization in a class of master-slave chaotic systems affected by bounded perturbations. The method provides the optimal state-feedback gain in terms of the minimal ellipsoid that guarantees minimum synchronization error bound. The problem of finding the optimal invariant ellipsoid is formulated in terms of a semi-definite programming problem that can be easily solved using various simulation and calculus tools. The effectiveness of the proposed criterion is illustrated by numerical simulations on the synchronization of Chua's systems.