Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI

Continuous case

Euntai Kim, Seungwoo Kim

Research output: Contribution to journalArticle

121 Citations (Scopus)

Abstract

A new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper. The method suggested herein is based on the numerical convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities (LMIs). The emphasis of this paper, however, is on the synthesis of fuzzy controller based on the derived stability condition. In synthesis, the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities (BMIs) and is solved numerically in an iterative manner. Fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains. Continuous iterative LMI (ILMI) approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system.

Original languageEnglish
Pages (from-to)391-400
Number of pages10
JournalIEEE Transactions on Fuzzy Systems
Volume10
Issue number3
DOIs
Publication statusPublished - 2002 Jun 1

Fingerprint

Fuzzy control
Fuzzy Control
Linear matrix inequalities
Fuzzy Systems
Affine Systems
Matrix Inequality
Linear Inequalities
Stability Analysis
Fuzzy systems
Control System
Synthesis
Control systems
Stability Condition
Controllers
Controller
Stabilizability
Formulation
Convex optimization
Numerical Optimization
Fuzzy Controller

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

Cite this

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Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI : Continuous case. / Kim, Euntai; Kim, Seungwoo.

In: IEEE Transactions on Fuzzy Systems, Vol. 10, No. 3, 01.06.2002, p. 391-400.

Research output: Contribution to journalArticle

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