Stability analysis for the polynomial fuzzy systems by utilizing equality constraints of sum-of-squares program

Ying Jen Chen, Kazuo Tanaka, Hua O. Wang, Hiroshi Ohtake, Wen June Wang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations

Abstract

This paper presents the stability analysis for polynomial fuzzy systems by utilizing the equality constraints of sum-of-squares (SOS) Program. Recently, T-S fuzzy systems have been extended to polynomial fuzzy systems, in which the consequent parts could be polynomial sub-systems. Moreover, stability and stabilization analyses for polynomial fuzzy systems have been done based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Since polynomials exist in the sub-systems and the positive definite matrices of the Lyapunov functions, the linear matrix inequality (LMI) tools are not valid for the polynomial analyses. Instead of LMI tools, SOSTOOLS of Matlab toolbox is applied to solve solutions for the polynomial analyses. The SOS program of SOSTOOLS can solve two kinds of constraints that are equality constraints and inequality constraints. The existing stability and stabilization analyses for polynomial fuzzy systems represent their conditions only in the inequality constraints. This paper analyzes the stability of the polynomial fuzzy systems by polynomial Lyapunov functions, and represents the new stability conditions not only in terms of the inequality constraints but also in terms of the equality constraints.

Original languageEnglish
Title of host publication2010 International Conference on System Science and Engineering, ICSSE 2010
Pages36-40
Number of pages5
DOIs
StatePublished - 2010
Event2010 International Conference on System Science and Engineering, ICSSE 2010 - Taipei, Taiwan
Duration: 1 Jul 20103 Jul 2010

Publication series

Name2010 International Conference on System Science and Engineering, ICSSE 2010

Conference

Conference2010 International Conference on System Science and Engineering, ICSSE 2010
Country/TerritoryTaiwan
CityTaipei
Period1/07/103/07/10

Keywords

  • Equality constraint
  • Polynomial fuzzy system
  • Polynomial lyapunov function
  • SOSTOOLS
  • Stability

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