Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay
Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay
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DOI：
10.1109/tac.2015.2404271
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发表时间：
2015-02
影响因子：
6.8
通讯作者：
Hongbing Zeng;Yong He;Min Wu;Jinhua She
中科院分区：
文献类型：
--
作者：
Hongbing Zeng;Yong He;Min Wu;Jinhua She
自由权矩阵和积分不等式方法被广泛用于推导时变时滞系统稳定性分析的时滞相关准则，因为它们避免了使用模型变换和边界交叉项技术。本技术说明提出了一个新的积分不等式，称为基于自由矩阵的积分不等式，进一步降低了这些方法的保守性。它包括著名的积分不等式作为特殊情况。利用它来研究时变时滞系统的稳定性，得到了保守性较小的时滞相关稳定性判据，这些判据以线性矩阵不等式的形式给出。两个数值算例验证了该方法的有效性和优越性。
The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.