Synchronization Criterion for Lur’e Systems via Delayed PD Controller
In this paper, 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, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.
KeywordsLur’e systems Synchronization Absolute stability PD controller LMIs Convex optimization
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- 6.Udwadia, F.E., Hosseini, M.A.M., Chen, Y.H.: Robust control of uncertain systems with time varying delays in control input. In: Proceedings of the American Control Conference, Albuquerque, New Mexico, pp. 3641–3644 (1997) Google Scholar
- 22.Skelton, R.E., Iwasaki, T., Grigoriadis, K.: A Unified Algebraic Approach to Linear Control Design. Talyor and Francis, London (1997) Google Scholar