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ℋ∞ Fuzzy Control for Systems with Repeated Scalar Nonlinearities

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Recent Advances in Intelligent Control Systems

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Abstract

This paper is concerned with the H ∞ control problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with repeated scalar nonlinearities. A modified T-S fuzzy model is proposed in which the consequent parts are composed of a set of discrete-time state equations containing a repeated scalar nonlinearity. Such a model can describe some well-known nonlinear systems such as recurrent neural networks. Attention is focused on the analysis and design of ℋ∞ fuzzy controllers with the same repeated scalar nonlinearities such that the closedloop T-S fuzzy control system is asymptotically stable and preserves a guaranteed H ∞ performance. Sufficient conditions are obtained for the existence of admissible controllers, and the cone complementarity linearization (CCL) procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities (LMIs), which can be solved efficiently by using existing optimization techniques. A illustrative example is provided to demonstrate the effectiveness of the results proposed in this chapter.

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Author information

Authors and Affiliations

  1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, 150001, Harbin, China

    Hongli Dong & Huijun Gao

  2. Department of Information Systems and Computing, Brunel University, UB8 3PH, Uxbridge, Middlesex, UK

    Zidong Wang

Authors
  1. Hongli Dong
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  2. Zidong Wang
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  3. Huijun Gao
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Editors and Affiliations

  1. Departamento de Control Automatico, CINVESTAV-IPN, Av. IPN 2508, 07360, México D.F., Mexico

    Wen Yu

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© 2009 Springer London

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Dong, H., Wang, Z., Gao, H. (2009). ℋ∞ Fuzzy Control for Systems with Repeated Scalar Nonlinearities. In: Yu, W. (eds) Recent Advances in Intelligent Control Systems. Springer, London. https://doi.org/10.1007/978-1-84882-548-2_3

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  • DOI: https://doi.org/10.1007/978-1-84882-548-2_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84882-547-5

  • Online ISBN: 978-1-84882-548-2

  • eBook Packages: EngineeringEngineering (R0)

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