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A Delay Decomposition Approach to Delay-Dependent Robust Passive Control for Takagi–Sugeno Fuzzy Nonlinear Systems

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Abstract

This paper is concerned with the problem of delay-dependent robust passive control for a fuzzy nonlinear system with time-varying delays. A Takagi–Sugeno fuzzy model approach is exploited to design a passive control for nonlinear systems with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov–Krasovskii functionals (LKFs) are constructed on these intervals. Employing these new LKFs, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of the time delay. We also design a state feedback controller that guarantees a robustly strictly passive closed-loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques.

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Acknowledgements

The work of authors was supported by Department of Science and Technology, New Delhi, India, under the sanctioned No. SR/S4/MS:485/07.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, 624 302, Tamilnadu, India

    P. Balasubramaniam & G. Nagamani

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  1. P. Balasubramaniam
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  2. G. Nagamani
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Correspondence to P. Balasubramaniam.

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Balasubramaniam, P., Nagamani, G. A Delay Decomposition Approach to Delay-Dependent Robust Passive Control for Takagi–Sugeno Fuzzy Nonlinear Systems. Circuits Syst Signal Process 31, 1319–1341 (2012). https://doi.org/10.1007/s00034-011-9384-8

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  • DOI: https://doi.org/10.1007/s00034-011-9384-8

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