Stability Analysis of Integral Delay Systems With Multiple Delays
Stability Analysis of Integral Delay Systems With Multiple Delays
复制标题
DOI：
10.1109/tac.2015.2426312
复制
发表时间：
2015-01
影响因子：
6.8
通讯作者：
Bin Zhou;Zhao‐Yan Li
中科院分区：
文献类型：
--
作者：
Bin Zhou;Zhao‐Yan Li
本文研究具有多时滞的积分时滞系统的稳定性分析。为了研究这一问题，将Jensen不等式推广到多项情况，为每项引入一个单独的松弛加权矩阵，并对其进行优化以降低保守性。利用多重Jensen不等式，通过发展一种新的线性化技术，建立了两种新的基于Lyapunov泛函的方法来获得用线性矩阵不等式（lmi）表示的充分稳定条件。结果表明，这些新条件总是比现有条件更不保守。此外，利用正算符理论，基于已有的耦合lmi表示的充分稳定性条件，得到了基于单个lmi的条件和基于谱半径的条件。数值算例说明了所提方法的有效性。
This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI-based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.