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Exponential stability and robust control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

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  • Yanbing Mao
  • Hongbin Zhang

Abstract

This paper deals with stability and robust H∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.

Suggested Citation

  • Yanbing Mao & Hongbin Zhang, 2014. "Exponential stability and robust control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(5), pages 1112-1127, May.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:5:p:1112-1127
    DOI: 10.1080/00207721.2012.745025
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    References listed on IDEAS

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    1. Dongsheng Du & Bin Jiang & Peng Shi, 2012. "Sensor fault estimation and compensation for time-delay switched systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(4), pages 629-640.
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