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 | |
| Publication status | Published - 2001 Feb 1 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Software
- Information Systems
- Human-Computer Interaction
- Computer Science Applications
- Electrical and Electronic Engineering
Cite this
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Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI : Discrete case. / Kim, Euntai; Kim, Dongyon.
In: IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 31, No. 1, 01.02.2001, p. 132-140.Research output: Contribution to journal › Letter
TY - JOUR
T1 - Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI
T2 - Discrete case
AU - Kim, Euntai
AU - Kim, Dongyon
PY - 2001/2/1
Y1 - 2001/2/1
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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UR - http://www.scopus.com/inward/citedby.url?scp=0035248625&partnerID=8YFLogxK
U2 - 10.1109/3477.907572
DO - 10.1109/3477.907572
M3 - Letter
VL - 31
SP - 132
EP - 140
JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
SN - 1083-4419
IS - 1
ER -