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Adaptive H ∞ synchronization of master-slave systems with mixed time-varying delays and nonlinear perturbations: An LMI approach

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Abstract

This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaptation law including the master-slave parameters are established for designing a delayed synchronization law in terms of linear matrix inequalities(LMIs). The time-varying controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. Particularly, it is shown that the synchronization speed can be controlled by adjusting the updated gain of the synchronization signal. Two numerical examples are given to demonstrate the effectiveness of the method.

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Authors and Affiliations

  1. Department of Engineering, Faculty of Engineering and Science, University of Agder, N-4898, Grimstad, Norway

    Hamid Reza Karimi

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Correspondence to Hamid Reza Karimi.

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Hamid Reza Karimi is a professor in control systems at the Faculty of Engineering and Science of the University of Agder in Norway. He is a senior member of IEEE and serves as a chairman of the IEEE chapter on control systems at IEEE Norway section. He is also serving as an editorial board member for some international journals, such as Mechatronics, Journal of the Franklin Institute, Neurocomputing, Mathematical Problems in Engineering, International Journal of Control, Automation and Systems, Journal of Innovative Computing Information and Control-Express Letters, International Journal of Control Theory and Applications, etc. He is a member of IEEE Technical Committee on Systems with Uncertainty, IFAC Technical Committee on Robust Control and IFAC Technical Committee on Automotive Control. He is the recipient of the Juan de la Cierva Research Award in 2008, Alexander-von-Humboldt-Stiftung Research Fellowship in 2006, German Academic Exchange Service (DAAD) Research Fellowship in 2003, National Presidency Prize for Distinguished Ph.D. student of Electrical Engineering in 2005, National Students Book Agency’s Award for Distinguished Research Thesis in 2007, etc.

His research interests include nonlinear systems, networked control systems, robust control/filter design, time-delay systems, wavelets and vibration control of flexible structures with an emphasis on applications in engineering.

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Karimi, H.R. Adaptive H ∞ synchronization of master-slave systems with mixed time-varying delays and nonlinear perturbations: An LMI approach. Int. J. Autom. Comput. 8, 381–390 (2011). https://doi.org/10.1007/s11633-011-0595-z

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  • DOI: https://doi.org/10.1007/s11633-011-0595-z

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