Technical communique: Stability and robust stability for systems with a time-varying delay
Technical communique: Stability and robust stability for systems with a time-varying delay
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DOI：
10.1016/j.automatica.2007.02.022
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发表时间：
2007-10
期刊：
影响因子：
--
通讯作者：
P. Park;J. Ko
中科院分区：
文献类型：
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作者：
P. Park;J. Ko
为了研究时变时滞系统的稳定性和鲁棒稳定性准则，本文不仅利用时变时滞状态x（t-h（t）），而且利用时滞上界状态x（t-h <$），充分利用当前状态x（t）、精确时滞状态x（t-h（t））、微小时滞状态x（t-h <$）和状态x的导数stec（t）之间关系的所有可能信息，在构造Lyapunov-Krasovskii泛函和一些适当的积分不等式时，最初由Park（1999.不确定定常时滞系统的时滞相关稳定性判据。IEEE自动控制学报，44（4），876-877）。两个基本的标准提供的情况下，没有界的延迟导数的假设和延迟导数的上界的假设。算例表明，所得准则优于文献中所有现有的准则。
To concern the stability and robust stability criteria for systems with time-varying delays, this note uses not only the time-varying-delayed state x(t-h(t)) but also the delay-upper-bounded state x(t-h¯) to exploit all possible information for the relationship among a current state x(t), an exactly delayed state x(t-h(t)), a marginally delayed state x(t-h¯), and the derivative of the state x˙(t), when constructing Lyapunov–Krasovskii functionals and some appropriate integral inequalities, originally suggested by Park (1999. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control, 44(4), 876–877). Two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed. Examples show the resulting criteria outperform all existing ones in the literature.