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Generalized projective synchronization in time-delayed systems: nonlinear observer approach. (English) Zbl 1311.34111

Summary: In this paper, we consider the projective-anticipating, projective, and projective-lag synchronization in a unified coupled time-delay system via nonlinear observer design. A new sufficient condition for generalized projective synchronization is derived analytically with the help of Krasovskii-Lyapunov theory for constant and variable time-delay systems. The analytical treatment can give stable synchronization (anticipatory and lag) for a large class of time-delayed systems in which the response system’s trajectory is forced to have an amplitude proportional to the drive system. The constant of proportionality is determined by the control law, not by the initial conditions. The proposed technique has been applied to synchronize Ikeda and prototype models by numerical simulation.{
©2009 American Institute of Physics}

MSC:

34D06 Synchronization of solutions to ordinary differential equations
93B51 Design techniques (robust design, computer-aided design, etc.)
34C28 Complex behavior and chaotic systems of ordinary differential equations
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