On the robust stability of interval time-delay systems - An application of the upper solution bounds of the Lyapunov equation
On the robust stability of interval time-delay systems - An application of the upper solution bounds of the Lyapunov equation
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DOI：
10.1016/j.jfranklin.2012.10.014
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发表时间：
2013-03
期刊：
影响因子：
--
通讯作者：
Chien-Hua Lee
中科院分区：
文献类型：
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作者：
Chien-Hua Lee
本文讨论了区间时滞系统的鲁棒稳定性检验问题。我们首先研究了连续代数李雅普诺夫方程（CALE）的上解界。通过使用线性代数技术，提出了一种简单的方法来获得新的上界的CALE。与现有的工作相比，这些新获得的界限是较少的限制，更容易计算。然后，我们应用它们来解决上述问题。利用李雅普诺夫方程方法，结合这些上界，给出了上述系统鲁棒稳定性和衰减率检验问题的新的简洁判据。与一些已知的时滞系统的结果相比，所得到的判据更尖锐。这些结果的一个有趣的后果是，它是没有必要解决任何李雅普诺夫方程，虽然李雅普诺夫方程的方法被使用。
In this paper, the robust stability test problem of the interval time-delay systems is discussed. We first study the upper solution bounds of the continuous algebraic Lyapunov equation (the CALE). By using linear algebraic techniques, a simple approach is proposed to derive new upper bounds of the CALE. Compared to existing works on this topic, these newly obtained bounds are less restrictive and easier to calculate. Then, we apply them to solve the mentioned problem. By using Lyapunov equation approach associated with these upper bounds, new concise criteria for the robust stability and decay rate test problem of the mentioned systems are presented. Comparing to some well-known results of the time-delay systems, the obtained criteria are sharper. An interesting consequence of these results is that it is not necessary to solve any Lyapunov equation although the Lyapunov equation approach is used.