Backstepping control and synchronization of chaotic time delayed systems

Abstract In this book chapter, novel backstepping controller and synchronization techniques for time delayed systems are proposed. One of the first contributions of this chapter is that backstepping control technique has not been extensively considered for the control of many kinds of time delayed complex systems, so the results of this study will be extended to the stabilization and synchronization of time delayed chaotic systems with state delays. Delays are a phenomenon found in many kinds of physical systems such as electrical and mechanical that can deteriorate or lead the system to instability. So, in the case of the stabilization of time delayed chaotic systems, it's important to drive the variables of the system to the equilibrium points that are directly related to their region of attraction, avoiding a chaotic behavior that can damage the physical system, this objective is achieved by appropriate backstepping controller design. Besides, a backstepping synchronization technique will be considered taking into account that the synchronization between coupled physical systems will be done accurately in the presence of time delays something that has not been considered before. To stabilize and synchronize time delayed chaotic systems, a novel backstepping controller technique will be considered avoiding the explosion of complexity to minimize the computational effort. In the stabilization and synchronization cases, delays in the states will be considered. The control and synchronization laws are determined by selecting appropriate Lyapunov functions following the steps of the backstepping design procedure.

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