LMI-Based Stability Analysis of Fuzzy-Model-Based Control Systems Using Approximated Polynomial Membership Functions
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then,...
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| Veröffentlicht in: | IEEE transactions on cybernetics 2011-06, Vol.41 (3), p.713-724 |
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| creator | Narimani, M Lam, H K Dilmaghani, R Wolfe, C |
| description | Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S -procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach. |
| doi_str_mv | 10.1109/TSMCB.2010.2086443 |
| format | Article |
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First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S -procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.</description><identifier>ISSN: 1083-4419</identifier><identifier>ISSN: 2168-2267</identifier><identifier>EISSN: 1941-0492</identifier><identifier>EISSN: 2168-2275</identifier><identifier>DOI: 10.1109/TSMCB.2010.2086443</identifier><identifier>PMID: 21095873</identifier><identifier>CODEN: ITSCFI</identifier><language>eng</language><publisher>United States: IEEE</publisher><subject>Algorithms ; Approximation ; Approximation methods ; Artificial Intelligence ; Computer Simulation ; Control systems ; Cybernetics ; Derivatives ; Feedback ; Fuzzy control ; Fuzzy Logic ; Fuzzy systems ; linear matrix inequality (LMI) ; Lyapunov functions ; Mathematical models ; membership-function-shape-dependent stability conditions ; Models, Statistical ; Numerical Analysis, Computer-Assisted ; Numerical stability ; Polynomials ; Shape ; Stability ; Stability analysis ; Studies ; Takagi-Sugeno (T-S) fuzzy model</subject><ispartof>IEEE transactions on cybernetics, 2011-06, Vol.41 (3), p.713-724</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S -procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Approximation methods</subject><subject>Artificial Intelligence</subject><subject>Computer Simulation</subject><subject>Control systems</subject><subject>Cybernetics</subject><subject>Derivatives</subject><subject>Feedback</subject><subject>Fuzzy control</subject><subject>Fuzzy Logic</subject><subject>Fuzzy systems</subject><subject>linear matrix inequality (LMI)</subject><subject>Lyapunov functions</subject><subject>Mathematical models</subject><subject>membership-function-shape-dependent stability conditions</subject><subject>Models, Statistical</subject><subject>Numerical Analysis, Computer-Assisted</subject><subject>Numerical stability</subject><subject>Polynomials</subject><subject>Shape</subject><subject>Stability</subject><subject>Stability analysis</subject><subject>Studies</subject><subject>Takagi-Sugeno (T-S) fuzzy model</subject><issn>1083-4419</issn><issn>2168-2267</issn><issn>1941-0492</issn><issn>2168-2275</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><sourceid>EIF</sourceid><recordid>eNqFkctKxDAUhoMo3l9AQYobV9Xc2ibLcfAGMyjMuC5p5lQjaTM2KVif3owzunDjKgn5_p_D-RA6IfiSECyv5rPp-PqS4vimWOScsy20TyQnKeaSbsc7FizlnMg9dOD9G8ZYYlnsoj0a45ko2D4Kk-lDeq08LJJZUJWxJgzJqFV28MYnrk5u-8_PIZ26BdgNN3Zt6JxNZoMP0Pjk2Zv2JRktl537MI0KEXlydmhdY5RNptBU0PlXs4xVrQ7Gtf4I7dTKejjenIdofnszH9-nk8e7h_FokmomSEipLHCd1UWmoZZaKs5VlVEBQKWsKwFSkFznbKGyiksgGYVcV1pwwWpFiGCH6GJdGyd778GHsjFeg7WqBdf7UgjJWU549j-ZC0wLUeBInv8h31zfxX2toIJHjvEI0TWkO-d9B3W57OJmuqEkuFypK7_VlSt15UZdDJ1tmvuqgcVv5MdVBE7XgAGA3-8sZyKnkn0Bmd-d-w</recordid><startdate>201106</startdate><enddate>201106</enddate><creator>Narimani, M</creator><creator>Lam, H K</creator><creator>Dilmaghani, R</creator><creator>Wolfe, C</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| source | IEEE Electronic Library (IEL) |
| subjects | Algorithms Approximation Approximation methods Artificial Intelligence Computer Simulation Control systems Cybernetics Derivatives Feedback Fuzzy control Fuzzy Logic Fuzzy systems linear matrix inequality (LMI) Lyapunov functions Mathematical models membership-function-shape-dependent stability conditions Models, Statistical Numerical Analysis, Computer-Assisted Numerical stability Polynomials Shape Stability Stability analysis Studies Takagi-Sugeno (T-S) fuzzy model |
| title | LMI-Based Stability Analysis of Fuzzy-Model-Based Control Systems Using Approximated Polynomial Membership Functions |
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