Abstract
This paper presents sliding mode control (SMC) technique for stabilization and synchronization of a class of chaotic/hyperchaotic systems in master–slave configuration. Here, a detailed procedure for deriving a single controller using SMC technique based proportional-integral sliding surface is proposed. Adaptation laws have been derived for the system parameters when the systems are subject to parametric uncertainties. Further, explicit criteria to decide the minimum number of control inputs required to meet out the desired operation of stabilization and synchronization is also proposed. Lyapunov stability theory is utilized to accomplish the desired objective. The proposed controller ensures the occurrence of sliding motion and achieves synchronization for the addressed class of chaotic/hyperchaotic systems in master–slave configuration. To validate the analytical results, example of four dimensional Lorenz–Stenflo hyperchaotic system is considered. Finally, detailed simulation results are provided to illustrate the effectiveness of the proposed controller.
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