T-S模糊广义时滞系统的耗散性及容许性分析

Dissipativity and Admissibility Analysis of T-S Fuzzy Descriptor Time-Delay Systems

针对T-S模糊广义时滞系统的耗散性及容许性分析问题,本文构造增广的非对称Lyapunov-Krasovskii(L-K)泛函,运用Jensen不等式及Wirtinger不等式,对L-K泛函进行估计,通过分析和推导得到了L-K泛函整体正定的条件,即不要求L-K泛函中的受限矩阵均为正定,放松了对这些矩阵的限制,然后对L-K泛函进行求导,结合积分不等式技术,以严格线性矩阵不等式(linear matrix inequalities,LMIs)的形式,给出了系统严格Q,S,R-γ-耗散以及容许的充分性条件,并通过2个数值例子验证所得结果在降低保守性时的有效性与优越性。数值仿真结果表明,与文献[12]及文献[14]中的对称L-K泛函方法相比,本文提出的非对称L-K泛函方法具有更低的保守性,说明了所提方法的有效性和优越性。广义时滞系统广泛应用于社会生活及各类工程系统,该研究具有重要的理论意义和实用价值。

This paper studies the dissipativity and admissibility analysis of T-S fuzzy descriptor time-delay systems.First,a novel asymmetric Lyapunov-Krasovskii(L-K)functional is constructed to obtain delay-dependent conditions.Then,Jensen′s inequality and Wirtinger′s inequality are used to estimate the L-K functional,and the overall positive definite condition of the L-K functional is obtained,in which the restrictive matrices in L-K functional are not required to be positive definite,and the restrictions on these matrices are relaxed.After that,the derivative of the L-K functional is bounded by using integral inequality techniques,and sufficiency conditions for the systems to be strictly Q,S,R-γ-dissipative and admissible are given in the form of strict linear matrix inequalities.Finally,the effectiveness and superiority of the proposed method are verified by two numerical examples.The numerical simulation results show that the asymmetric L-K functional method proposed in this paper is less conservative than the symmetric L-K functional method in literature[12]as well as in the literature[14],which show the effectiveness and superiority of the proposed method.Descriptor time-delay systems are widely used in social life and various engineering systems,so this research has important theoretical significance and practical value.