Asymptotic Properties of Stochastic Delay Systems
Asymptotic Properties of Stochastic Delay Systems
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随机时滞系统的渐近性质
DOI：
10.1007/978-3-642-18482-6_28
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Erik I. Verriest
中科院分区：
文献类型：
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作者：
Erik I. Verriest
本文对随机时滞系统的理论作了一个简单而简单的介绍。首先介绍了离散情况下的稳定性问题。从动力学的角度来看，这类系统更简单，因为它们仍然是有限维度的，因此为即将到来的事情提供了一个‘Wann-up’。由于连续时间随机系统是用它演算的语言来分析的，因此对后者作了一个初步的介绍，使这些注记是自成体系的。给出了时滞无关和时滞相关的随机稳定性条件。其中一些是新的。在没有均衡的情况下，不变分布可能仍然存在。讨论了定常Fokker-Planck方程的存在条件。这些结果进一步推广到随机中立型系统。终于来了。提出了一种新的在没有精确时滞信息的情况下动态控制器的实用设计方法。
A gentle and elementary introduction to the theory of stochastic lime delay systems is presented in this contribution. First an introduction to the stability problem in the discrete case is given. This class of systems is simpler from a dynamical point of view, as they remain finite dimensional, and provide thus a ‘wann-up’ for what is to come. Since continuous time stochastic systems are analyzed in the language of Itô-calculus, an elementary introduction to the latter is included to make these notes self-contained. Delay-independent and delay dependent conditions for stochastic stability arc derived. Some of these are new. In the absence of equilibria, invariant distributions may still exist. Existence conditions, and the stationary Fokker-Planck equation are discussed. These results are further extended to the class of stochastic neutral systems. Finally. a new realistic design procedure is suggested for dynamic controllers in the absence of precise delay information.