论文标题
具有延迟的非自主混合随机系统
Non-autonomous hybrid stochastic systems with delays
论文作者
论文摘要
本文的目的是研究具有延迟的非自主随机混合系统的动态行为。通过一般的Krylov-Bogolyubov方法，我们首先获得了存在非自治随机系统的进化系统的足够条件，还提供了一些易于证实的条件。然后，随着延迟接近零，我们证明了度量进化系统的足够条件。作为抽象理论的应用，我们首先证明了随机系统延迟的随机系统的演变系统的存在，该系统来自基于离散时间状态观察的反馈控制问题。此外，当观察间隔变为零时，我们显示了一系列非自治随机系统的演变系统的每个限制点必须是限制系统测量的进化系统。
The aim of this paper is to study the dynamical behavior of non-autonomous stochastic hybrid systems with delays. By general Krylov-Bogolyubov's method, we first obtain the sufficient conditions for the existence of an evolution system of measures of the non-autonomous stochastic system and also give some easily verifiable conditions. We then prove a sufficient condition for convergence of evolution systems of measures as the delay approaches zero. As an application of the abstract theory, we first prove the existence of evolution systems of measures for stochastic system with time-vary delays, which comes from feedback control problem based on discrete-time state observations. Furthermore, when observation interval goes to zero, we show every limit point of a sequence of evolution system of measures of the non-autonomous stochastic system must be a evolution system of measures of the limiting system.
