Globally Stable Synchronization of Chaotic Systems Based on Norm Observers Connected in Cascade

The synchronization of chaotic systems is achieved using output-feedback sliding mode control even in the presence of disturbances. Norm observers connected in cascade estimate upper bounds of the state variables required for the realization of the control law. This approach allows the proof of global stability and exponential convergence of the state errors based on Lyapunov's stability theory and input-to-state-stability properties of a broad class of chaotic systems. Thus, the global synchronization is guaranteed such that the initial conditions of the master (transmitter) and slave (receiver) systems can be arbitrary. The unified formulation of the chaotic systems with time-varying parameters allows periodic switching between Lorenz and Chen attractors. Simulation results illustrate the fast synchronization of master-slave chaotic oscillators and their application to a secure communication system using a time-varying cryptographic key and nonlinear encryption functions, which improve the privacy of the proposed scheme.