Novel stability conditions for discrete-time T-S fuzzy systems: A Kronecker-product approach

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• 作者：Jun Chen^a ; ^b ; Shengyuan Xu ; ^a ; ^{syxu@njust.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{syxu02@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Baoyong Zhang^a ; Zhidong Qi^a ; Ze Li^c
• 关键词：Stability ; Takagi&ndash ; Sugeno fuzzy system ; Homogeneous matrix polynomial ; Linear matrix inequality ; Kronecker product
• 刊名：Information Sciences
• 出版年：2016
• 出版时间：10 April 2016
• 年：2016
• 卷：337-338
• 期：Complete
• 页码：72-81
• 全文大小：367 K

文摘

This paper is concerned with the issue of developing a novel strategy to reduce the conservatism of stability conditions for discrete-time Takagi–Sugeno (T–S) fuzzy systems. Unlike the previous ones which are almost quadratic with respect to the state vector, a new class of Lyapunov functions is proposed which is quadratic with respect to the Kronecker products of the state vector, thus including almost the existing ones found in the literature as special cases. By combining the characterizations of homogeneous matrix polynomials and the properties of membership functions, relaxed stability conditions are derived in the form of linear matrix inequalities which can be efficiently solved by the convex optimization techniques. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.