Analysis and design of an affine fuzzy system via bilinear matrix inequality

Euntai Kim, Chang Hoon Lee, Young Wan Cho

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

In this paper, a novel analysis and design method for affine fuzzy systems is proposed. Both continuous-time and discrete-time cases are considered. The quadratic stability and stabilizability conditions of the affine fuzzy systems are derived and they are represented in the formulation of bilinear matrix inequalities (BMIs). Two diffeomorphic state transformations (one is linear and the other is nonlinear) are introduced to convert the plant into more tractable affine form. The conversion makes the stability and stabilizability problems of the affine fuzzy systems convex and makes the problems solvable directly by the convex linear matrix inequality (LMI) technique. The bias terms of the fuzzy controller are solved simultaneously together with the gains. Finally, the applicability of the suggested method is demonstrated via an example and computer simulation.

Original languageEnglish
Pages (from-to)115-123
Number of pages9
JournalIEEE Transactions on Fuzzy Systems
Volume13
Issue number1
DOIs
Publication statusPublished - 2005 Feb 1

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Affine Systems
Fuzzy systems
Fuzzy Systems
Matrix Inequality
Stabilizability
Quadratic Stability
Fuzzy Controller
Linear matrix inequalities
Design Method
Convert
Continuous Time
Linear Inequalities
Discrete-time
Computer Simulation
Controllers
Formulation
Computer simulation
Term
Design

All Science Journal Classification (ASJC) codes

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

Cite this

Kim, Euntai ; Lee, Chang Hoon ; Cho, Young Wan. / Analysis and design of an affine fuzzy system via bilinear matrix inequality. In: IEEE Transactions on Fuzzy Systems. 2005 ; Vol. 13, No. 1. pp. 115-123.
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Analysis and design of an affine fuzzy system via bilinear matrix inequality. / Kim, Euntai; Lee, Chang Hoon; Cho, Young Wan.

In: IEEE Transactions on Fuzzy Systems, Vol. 13, No. 1, 01.02.2005, p. 115-123.

Research output: Contribution to journalArticle

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