A Generalized Analytical Approach for the Synchronization of Multiple Chaotic Systems in the Finite Time

This paper proposes a new finite-time controller that realizes multi-switching synchronization of chaotic systems with bounded disturbances using the drive and response system synchronization arrangement. The finite-time controller derives the synchronization error to zero within a specified time. The proposed controller consists of three basic terms; each of them accomplishes a distinct objective: (1) stability of the control loop, (2) smooth and fast convergence behavior of the synchronization error, and (3) disturbance rejection. This study also devises a methodology for designing the finite-time controller and describes a general approach that furnishes a systematic procedure for the analysis of the closed loop. The smooth behavior terminology introduced in (2) refers to the over-damped convergence of the synchronization error signals to zero and the synthesis of chattering-free control effort. The analysis, which assures the global stability of the closed loop, uses the second stability theorem of the Lyapunov, while the finite-time stability technique determines the finite-time convergence. This paper includes simulations of two numerical examples for the validation of the theoretical findings and discusses the comparative analysis. The proposed methodology is suitable to design controllers for a wide range of hyper(chaotic) systems. The contributions of the paper are: (1) describe an innovative generalize analytical methodology for the multi-switching combination synchronization of chaotic systems and (2) propose a novel controller design that insures the finite-time synchronization.