Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi-Sugeno's form

  • Authors:

  • Baocang Ding;Biao Huang

  • Affiliations:

  • College of Automation, Chongqing University, Chongqing, P. R. China;Department of Chemical and Materials Engineering, University of Alberta, Edmonton, T6G 2G6 Canada

  • Venue:
  • International Journal of Systems Science
  • Year:
  • 2008

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Abstract

This article addresses the stabilisation of non-linear systems represented by a discrete-time Takagi-Sugeno model. Based on an extended non-quadratic Lyapunov function and a non-parallel distributed compensation (non-PDC) law, some additional slack matrices are introduced. Compared with the existing methods, which collect the interactions among the subsystems into a sequence of collection matrices, the new method re-collects the newly introduced slack matrices into another collection matrix. In this way, a stability result more relaxed than some existing ones are obtained. Further, the convexity of the fuzzy blending rules is utilised, with a further improved result obtained. The corresponding robust stability results are also proposed. The effectiveness of the new results is validated by two simulation examples.