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Relaxed stabilisation criterion for discrete T–S fuzzy systems by minimum-type piecewise non-quadratic Lyapunov function

Relaxed stabilisation criterion for discrete T–S fuzzy systems by minimum-type piecewise non-quadratic Lyapunov function

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  • Author(s): Y.-J. Chen 1 ; H. Ohtake 2 ; K. Tanaka 2 ; W.-J. Wang 1 ; H.O. Wang 3
    • View affiliations
    • Affiliations: 1: Department of Electrical Engineering, National Central University, Jhongli, Taiwan
      2: Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Tokyo, Japan
      3: Department of Aerospace and Mechanical Engineering, Boston University, Boston, USA
  • Source: Volume 6, Issue 12, 16 August 2012, p. 1918 – 1925
    DOI:  10.1049/iet-cta.2010.0697 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

Piecewise Lyapunov functions and non-quadratic Lyapunov functions have been employed to analyse Takagi–Sugeno (T–S) fuzzy systems for getting relaxed results in the literature. Nevertheless, until now piecewise non-quadratic Lyapunov functions have not been used to design T–S fuzzy control systems. Motivated by the aforementioned concerns, this study utilises the minimum-type piecewise non-quadratic Lyapunov function to design the discrete T–S fuzzy control system. Based on the piecewise non-quadratic Lyapunov function, the switching non-parallel distributed compensation control law is proposed to obtain the relaxed stabilisation criterion. Owing to that some conditions of the proposed criterion are bilinear matrix inequalitiy conditions, the particle swarm optimisation algorithm is applied for finding out the solution of the criterion. An example is provided to illustrate the effectiveness of the proposed criterion.

Inspec keywords: control system synthesis; distributed control; fuzzy control; piecewise linear techniques; stability; discrete systems; particle swarm optimisation; Lyapunov methods; compensation

Other keywords: switching nonparallel distributed compensation control law; T-S fuzzy control system design; bilinear matrix inequalitiy conditions; minimum-type piecewise nonquadratic Lyapunov function; particle swarm optimisation algorithm; relaxed stabilisation criterion; discrete T-S fuzzy systems; Takagi-Sugeno fuzzy systems

Subjects: Discrete control systems; Optimisation techniques; Control system analysis and synthesis methods; Stability in control theory; Fuzzy control

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