Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: Discrete case

Euntai Kim; Dongyon Kim

doi:10.1109/3477.907572

Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: Discrete case

Euntai Kim, Dongyon Kim

Department of Electrical and Electronic Engineering

Research output: Contribution to journal › Letter › peer-review

106 Citations (Scopus)

Abstract

This paper develops a stability analysis and controller synthesis methodology for a discrete affine fuzzy system based on the convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived. Then, the condition is recast in the formulation of Linear Matrix Inequalities (LMI) and numerically addressed. 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 non-convex matrix inequalities and is solved numerically in an iterative manner. Discrete iterative LMI (ILMI) approach is proposed to obtain the feasible solution for the synthesis of the affine fuzzy system. Finally, the applicability of the suggested methodology is demonstrated via some examples and computer simulations.

Original language	English
Pages (from-to)	132-140
Number of pages	9
Journal	IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume	31
Issue number	1
DOIs	https://doi.org/10.1109/3477.907572
Publication status	Published - 2001 Feb

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Software
Information Systems
Human-Computer Interaction
Computer Science Applications
Electrical and Electronic Engineering

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abstract = "This paper develops a stability analysis and controller synthesis methodology for a discrete affine fuzzy system based on the convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived. Then, the condition is recast in the formulation of Linear Matrix Inequalities (LMI) and numerically addressed. 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 non-convex matrix inequalities and is solved numerically in an iterative manner. Discrete iterative LMI (ILMI) approach is proposed to obtain the feasible solution for the synthesis of the affine fuzzy system. Finally, the applicability of the suggested methodology is demonstrated via some examples and computer simulations.",

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T1 - Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI

T2 - Discrete case

AU - Kim, Euntai

AU - Kim, Dongyon

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N2 - This paper develops a stability analysis and controller synthesis methodology for a discrete affine fuzzy system based on the convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived. Then, the condition is recast in the formulation of Linear Matrix Inequalities (LMI) and numerically addressed. 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 non-convex matrix inequalities and is solved numerically in an iterative manner. Discrete iterative LMI (ILMI) approach is proposed to obtain the feasible solution for the synthesis of the affine fuzzy system. Finally, the applicability of the suggested methodology is demonstrated via some examples and computer simulations.

AB - This paper develops a stability analysis and controller synthesis methodology for a discrete affine fuzzy system based on the convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived. Then, the condition is recast in the formulation of Linear Matrix Inequalities (LMI) and numerically addressed. 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 non-convex matrix inequalities and is solved numerically in an iterative manner. Discrete iterative LMI (ILMI) approach is proposed to obtain the feasible solution for the synthesis of the affine fuzzy system. Finally, the applicability of the suggested methodology is demonstrated via some examples and computer simulations.

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