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Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

Author

Listed:
  • Alireza Nasiri
  • Sing Kiong Nguang
  • Akshya Swain
  • Dhafer Almakhles

Abstract

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Suggested Citation

  • Alireza Nasiri & Sing Kiong Nguang & Akshya Swain & Dhafer Almakhles, 2018. "Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 557-566, February.
  • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:3:p:557-566
    DOI: 10.1080/00207721.2017.1407006
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