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Synchronization criterion for Lur’e systems via delayed PD controller. (English) Zbl 1202.93138

Summary: The effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback Proportional-Derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur’e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, a stability condition is obtained via the linear matrix inequalities (LMI) formulation. The condition represented in the terms of LMIs can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.

MSC:

93D20 Asymptotic stability in control theory
93D21 Adaptive or robust stabilization
34H10 Chaos control for problems involving ordinary differential equations
93C25 Control/observation systems in abstract spaces
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