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Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. (English) Zbl 1253.93017
Summary: This paper brings attention to the chaotic antisynchronization and synchronization for a novel class of chaotic systems with different structure and dimensions by using a new sliding mode control strategy. This approach needs only $$n-1$$ controllers, where $$n$$ is the number of the salve system dimensions. And our method uses Proportional Integral (PI) surface and saturation function to simplify the task of assigning the performance of the closed-loop error system in sliding motion. Furthermore, sufficient conditions are derived, and representative examples are proposed as well. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the proposed control scheme, which are in agreement with theoretical analysis.

##### MSC:
 93B12 Variable structure systems 34D06 Synchronization of solutions to ordinary differential equations 93C10 Nonlinear systems in control theory
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