Synchronization Criterion for Lur’e Systems via Delayed PD Controller

D. H. Ji (), Ju H. Park (), S. M. Lee, J. H. Koo and S. C. Won
Additional contact information
D. H. Ji: Samsung Electronics
Ju H. Park: Yeungnam University
S. M. Lee: Daegu University
J. H. Koo: POSTECH
S. C. Won: POSTECH

Journal of Optimization Theory and Applications, 2010, vol. 147, issue 2, No 6, 298-317

Abstract: Abstract 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.

Keywords: Lur’e systems; Synchronization; Absolute stability; PD controller; LMIs; Convex optimization (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-010-9723-0

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