Finite-frequency model reduction of discrete-time T-S fuzzy state-delay systems

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• 作者：Da-Wei Ding^a ; ^{dingdawei@ustb.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Xiangpeng Xie^b ; ^{xiexiangpeng1953@sina.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Xin Du^c ; ^{duxin@shu.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Xiao-Jian Li^d ; ^{lixiaojian@ise.neu.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Model reduction ; T&ndash ; S fuzzy systems ; Time delay ; Finite frequency
• 刊名：Neurocomputing
• 出版年：2016
• 出版时间：26 August 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：121-128
• 全文大小：496 K

文摘

This paper is concerned with the problem of model reduction for discrete-time Takagi–Sugeno (T–S) fuzzy state-delay systems with finite-frequency input signals. A new finite-frequency model reduction algorithm is proposed, which can get a better approximation performance than the existing full-frequency methods. Firstly, a finite-frequency class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0925231216302697&_mathId=si0002.gif&_user=111111111&_pii=S0925231216302697&_rdoc=1&_issn=09252312&md5=54559cc87a6e56c404c76208dfa5cabb" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ performance index is defined in the frequency domain. Then, a stability condition and a finite-frequency class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0925231216302697&_mathId=si0002.gif&_user=111111111&_pii=S0925231216302697&_rdoc=1&_issn=09252312&md5=54559cc87a6e56c404c76208dfa5cabb" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ performance analysis condition are developed by the aid of Jensen׳s inequality and Parseval׳s theorem, respectively. Based on these conditions, sufficient model reduction conditions are derived for discrete-time T–S fuzzy state-delay systems. An optimization algorithm is proposed to obtain a stable reduced-order model satisfying the finite-frequency performance specification. Finally, the effectiveness of the proposed method is illustrated by a numerical example.