Improved stability and instability theorems for stochastic nonlinear systems
Improved stability and instability theorems for stochastic nonlinear systems
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DOI：
10.1002/rnc.4924
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发表时间：
2020-02
影响因子：
3.9
通讯作者：
Liqiang Yao;Weihai Zhang
中科院分区：
文献类型：
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作者：
Liqiang Yao;Weihai Zhang
本文研究了随机非线性系统稳定和不稳定的充分条件。利用一致渐近稳定函数，提出了一系列新的稳定性(不稳定性)判据，这些判据允许Lyapunov(Lyapunov-like或Chetaev)函数的无穷小算子是不定的。所得到的稳定性和不稳定性定理分别削弱了对Lyapunov和Lyapunov-like(或Chetaev)函数的约束。现有的许多经典稳定性和失稳判据都可以看作是本文稳定性和失稳结果的特例。最后，通过仿真算例验证了理论结果的正确性。
This paper focuses on sufficient conditions which make stochastic nonlinear systems stable and unstable. A series of new stability (instability) criteria, which admit the infinitesimal operator of Lyapunov (Lyapunov‐like or Chetaev) functions to be indefinite, are proposed using the uniformly asymptotically stable function. The obtained stability and instability theorems weaken the constraints on Lyapunov and Lyapunov‐like (or Chetaev) functions, respectively. Many existing classical stability and instability criteria can be regarded as special cases of the stability and instability results in this paper. Finally, the presented theoretical results are illustrated by some simulation examples.