Control Synthesis of Discrete-Time T-S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach
This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-depen...
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| Veröffentlicht in: | IEEE transactions on cybernetics 2016-03, Vol.46 (3), p.630-640 |
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| creator | Xie, Xiangpeng Yue, Dong Zhang, Huaguang Xue, Yusheng |
| description | This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper. |
| doi_str_mv | 10.1109/TCYB.2015.2411336 |
| format | Article |
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A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. 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A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.</description><subject>Control systems</subject><subject>Cybernetics</subject><subject>Frequency modulation</subject><subject>Fuzzy</subject><subject>Fuzzy systems</subject><subject>Homogenous matrix polynomials</subject><subject>Linear matrix inequalities</subject><subject>Lyapunov functions</subject><subject>Lyapunov methods</subject><subject>multiinstant</subject><subject>Polynomials</subject><subject>reducing conservatism</subject><subject>slack variable</subject><subject>Stabilization</subject><subject>stabilization conditions</subject><subject>Symmetric matrices</subject><subject>Synthesis</subject><subject>Weighting functions</subject><issn>2168-2267</issn><issn>2168-2275</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkU1PGzEQhq2qqCDgB1SVkKVeetng8fceIS0fEggk0kNPK8eZhUW767D2Vgq_HkcJOXDBl7HsZ-admZeQ78AmAKw8nU3_nU84AzXhEkAI_YUccNC24Nyor7u7NvvkOMZnlo_NT6X9Rva5slwwJQ_I4zT0aQgtfVj16QljE2mo6e8m-gETFrOmQzorHujF-Pq6ylBM2EX6v3HU0duxTU1x3cfk-kSvQhcesQ9jpPehXfWha1xLz5bLITj_dET2atdGPN7GQ_L34s9selXc3F1eT89uCi8sT4VBrxBKU3MmgCNqycQcmfYgBXhcgNLSKa9rqeo5XyAaZxnWYOS89AvDxSH5tambZV9GjKnq8izYtq7H3FoFeQfMSqXE56jRhlkmSsjozw_ocxiHPg-SKZtlQcu1NmwoP4QYB6yr5dB0blhVwKq1Z9Xas2rtWbX1LOecbCuP8w4Xu4x3hzLwYwM0iLj7Nkwrnnt7AzfgmZc</recordid><startdate>201603</startdate><enddate>201603</enddate><creator>Xie, Xiangpeng</creator><creator>Yue, Dong</creator><creator>Zhang, Huaguang</creator><creator>Xue, Yusheng</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Control systems Cybernetics Frequency modulation Fuzzy Fuzzy systems Homogenous matrix polynomials Linear matrix inequalities Lyapunov functions Lyapunov methods multiinstant Polynomials reducing conservatism slack variable Stabilization stabilization conditions Symmetric matrices Synthesis Weighting functions |
| title | Control Synthesis of Discrete-Time T-S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach |
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