A non-quadratic Lyapunov functional for H_∞ control of nonlinear systems via Takagi-Sugeno models

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• 作者：Raymundo Má ; rquez^a ; ^b ; ^{raymundo.marquez@itson.edu.mx" class="auth_mail" title="E-mail the corresponding author} ; Thierry Marie Guerra^a ; ^{guerra@univ-valenciennes.fr" class="auth_mail" title="E-mail the corresponding author} ; Miguel Bernal^b ; ^{miguel.bernal@itson.edu.mx" class="auth_mail" title="E-mail the corresponding author} ; Alexandre Kruszewski^c ; ^{alexandre.kruszewski@ec-lille.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of The Franklin Institute
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：353
• 期：4
• 页码：781-796
• 全文大小：620 K

文摘

This paper presents a novel non-quadratic Lyapunov functional with time delay for controller design and 16003216000168&_mathId=si0013.gif&_user=111111111&_pii=S0016003216000168&_rdoc=1&_issn=00160032&md5=98777af125888eea9e623918dbd57480" title="Click to view the MathML source">H_∞$H_{\infty }$ disturbance rejection for nonlinear systems. Based on an exact Takagi–Sugeno representation of the nonlinear model, a proper integral structure for Lyapunov-based design allows circumventing the well-known problem of handling the time derivatives of the membership functions without imposing additional requirements. The methodology proposed that both increase the complexity of the classical quadratic LMI design and the control law structure, but in a reasonable manner. The main advantages are that the conditions in the proposed approach are expressed as linear matrix inequalities and proven to outperform previous results on the same subject. Illustrative examples are included to point out the aforementioned contributions.