Robust Synchronization of Chaotic Nonlinear Systems Subjected to Input Saturation by Employing Nonlinear Observers-Based Chaos Synchronization Methodology

This paper proposes coupled chaotic synchronous (CCS) observers-based synchronization methodologies to synchronize the leader and follower uncertain nonlinear chaotic systems. Simultaneous synthesis of observer and controller is suggested for the estimation of the states and synchronization of the leader–follower systems, respectively. The estimated synchronization error converges to zero exponentially by using CCS observer and the state estimation error approaches zero by utilizing the feedback controller to guarantee synchronization in addition to state estimation. By utilizing Lyapunov functional, Lipschitz properties of nonlinear dynamics, local sector condition of dead-zone nonlinearity, and gain bounded properties of the exogenous disturbances, nonlinear matrix inequalities-based sufficient conditions are provided for the convergence of the estimated state and synchronization error to zero. Two-step matrix inequality-based methodology is derived for finding the controller and observer gain matrices. Application to uncertain chaotic nonlinear FitzHugh–Nagumo neurons under input saturation and disturbances reveals the effectiveness of the proposed control methodology.