Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

  • Authors:
  • Xiaoming Chen;James Lam;Huijun Gao;Shaosheng Zhou

  • Affiliations:
  • Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, Hong Kong;Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, Hong Kong;Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China 150001;Department of Automation, Hangzhou Dianzi University, Hangzhou, China 310018

  • Venue:
  • Multidimensional Systems and Signal Processing
  • Year:
  • 2013

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Abstract

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini---Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.