Robust H∞ fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps: An LMI approach

  • Authors:

  • Wudhichai Assawinchaichote;Sing Kiong Nguang;Peng Shi

  • Affiliations:

  • The Department of Electronic and Telecommunication Engineering, King Mongkut's University of Technology Thonburi, 91 Suksawads 48 Rd., Bangkok 10140, Thailand;The Department of Electrical and Computer Engineering, The University of Auckland, Private Bag 92019 Auckland, New Zealand;Division of Mathematics and Statistics, School of Technology, University of Glamorgan, Pontypridd, Wales, CF37 1DL, UK

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

This paper examines the problem of designing a robust H"~ fuzzy filter for a singularly perturbed Takagi-Sugeno (TS) fuzzy system with Markovian jumps. Based on a linear matrix inequality (LMI) approach, sufficient conditions for the existence of a robust H"~ fuzzy filter are derived in terms of a family of LMIs. To alleviate the numerical stiffness resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation @e. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied to both standard and nonstandard nonlinear singularly perturbed systems. A numerical example is provided to illustrate the design developed in this paper.