随机时滞非线性微分系统的均方BIBO稳定

This project aims to discuss the problem of bounded input bounded output (BIBO) stability of stochastic delay differential systems with non-linear perturbations. The research mainly includes: the problem of mean square BIBO stability of continuous time stochastic delay differential systems with non linear perturbations. According to proposed by the Lyapunov stability theory, by adopting the Razumikhin method, L operator and comparison principle to discuss the mean square BIBO stability of stochastic nonlinear systems with discrete and distributed delays; To study the problem of mean square BIBO stability of discrete time stochastic systems with delays and non-linear perturbations, it should be considered that the system is a discrete system but containing distributed delays; To study the problem of mean square BIBO stability of stochastic nonlinear differential systems with random variable delays, the keypoint we should take into consideration is that the delay is a Bernoulli random variable. Since stochastic time-delay nonlinear differential systems possesses a profound and extensive application background, the relevant theoretical results have broad application prospects.

本项目旨在探讨具有非线性扰动的随机时滞微分系统的有界输入-有界输出(BIBO)稳定性问题。研究内容主要包括：连续时间随机时滞非线性微分系统的均方BIBO稳定性问题，拟通过Lyapunov稳定性理论，采用Razumikhin方法结合L算子和比较原理探讨含离散时滞和分布时滞的随机非线性系统均方BIBO稳定性问题；研究离散时间随机时滞非线性微分系统的均方BIBO稳定性问题，分析系统是离散系统且含有分布时滞情况下系统的均方BIBO稳定性问题；研究时滞为随机变量的随机非线性微分系统的均方BIBO稳定性问题，重点研究时滞为Bernoulli随机变量的随机系统的均方BIBO稳定性。由于随机时滞非线性微分系统的深刻而广泛的应用背景，相应的理论结果具有广阔的应用前景

本项目主要利用随机微分方程理论、泛函微分方程理论、Lyapunov稳定理论及控制理讨论具有非线性扰动的随机时滞系统的有界输入-有界输出(BIBO)稳定性问题。项目围绕具有非线性扰动的随机微分动力系统的均方BIBO稳定性问题，就时滞为连续时滞、离散时滞及时滞为Bernoulli随机变量三种情况分别进行研究。. 项目自从2013年1月立项以来，发表(含录用)科研论文9篇，其中SCI检索4篇，EI检索１篇，国内重要期刊发表论文４篇。项目主要做了四部分工作，分别为：第一部分研究时滞为函数变量的连续时间随机非线性系统的BIBO稳定性问题；第二部分研究时滞为函数变量的离散时间随机非线性系统的BIBO稳定性问题；第三部分研究时滞为Bernoulli随机变量的非线性系统的BIBO稳定性问题；第四部分研究了系统为网络化控制系统的BIBO稳定性问题及控制器的设计问题。