具有随机输入的混合复合动态系统的稳定性判据(英文)

Stability Criteria for Hybrid Composite Dynamical Systems with Random Inputs

本文给出了如图1所示的具有随机输入的混合复合动态系统的稳定性分析,所讨论的系统由一个算子L和一个随机微分方程描述的方块组成。对于这样的系统,我们建立了随机吸引性、随机渐近稳定性、随机有界性、大范围随机渐近稳定性、p吸引性、渐近p稳定性、一致p有界性和大范围渐近p稳定性的判据。这些判据包含了一些假设,这些假设描述了算子L和整个系统的定性I/O性质和表示了由随机微分方程描述的子系统的性质。

The stability analysis is given for hybrid composite dynamical systems with random inputs which are depicted in Fig. 1, consisting of an operator L and a block described by a system of stochastic differential equations. Criteria are established for attractivity in probability, asymptotic stability in probability, uniform boundedncss in probability, asymptotic stability in probability in the large, p-attractivity, asymptotic p-stability, uniform p-boundedncss, and asymptotic p-stability in the large for such systems. These criteria involve hypotheses which characterize the qualitative I/O properties of the operator L and of the entire system, and which express the Lyapunov stability properties of the subsystem described by the indicated stochastic differential equations.