几类随机耦合系统的稳定性

发布时间：2018-03-03 10:57

本文选题：耦合系统　切入点：白噪声　出处：《哈尔滨工业大学》2016年博士论文　论文类型：学位论文

【摘要】：近年来,耦合系统的稳定性吸引了许多学者的关注,很多确定性耦合系统稳定性的重要结果已经出现。然而,实际的耦合系统总是受到各种环境噪声的干扰,而环境噪声会使系统的稳定性发生改变。从控制理论的观点看,研究随机耦合系统的稳定性非常重要。本文致力于建立几类随机耦合系统的数学模型,使用随机分析方法分析其稳定性,揭示环境噪声和耦合结构对其稳定性的影响。论文的主要研究内容包括:1.通过把多扩散和白噪声引入到多斑块模型中,建立具有多扩散的随机多斑块模型。结合图论和Lyapunov方法,得到模型指数稳定的Lyapunov型准则和系数型判据,并应用系数型判据分析随机耦合振子的均方指数稳定性。研究结果表明:在有向图的拓扑结构满足一定条件和白噪声强度在一定范围时,随机模型是稳定的。2.建立具有多扩散的比例时滞随机多斑块模型,分析模型的指数稳定性,得到Lyapunov型准则和系数型判据,并应用系数型判据研究比例时滞随机耦合振子的均方指数稳定性。研究结果表明:模型的指数稳定性与白噪声的强度,比例时滞的系数和有向图的拓扑结构都有紧密联系。3.结合图论和Lyapunov方法,研究具有多扩散的随机多斑块模型的输入状态稳定性,得到输入状态稳定的充分准则,并研究具有输入控制的随机耦合振子的输入状态稳定性。研究结果表明:在适当的白噪声强度下,模型的输入状态稳定性不仅和顶点系统的输入状态稳定性有关,而且和有向图的拓扑结构有关。4.结合Razumikhin方法和图论,研究网络上耦合中立型随机时滞系统的稳定性,得到矩指数稳定的Razumikhin型准则和系数型判据,以及几乎确定指数稳定准则,并给出数值算例验证理论结果的有效性。研究结果表明:系统的指数稳定性依赖于白噪声的强度和有向图的强连通性。5.应用Lyapunov方法和M矩阵理论,分析具有无穷时滞和Markov转换的随机神经网络的随机稳定性、随机渐近稳定性和全局随机渐近稳定性,得到保证模型三种随机稳定的充分条件。研究结果表明:当白噪声的强度在一定范围时,模型的三种随机稳定性与Markov链的生成矩阵密切相关。
[Abstract]:In recent years, the stability of coupled systems has attracted the attention of many scholars, and many important results of the stability of deterministic coupled systems have emerged. However, the actual coupled systems are always disturbed by various kinds of environmental noise. From the point of view of control theory, it is very important to study the stability of stochastic coupled systems. Stochastic analysis is used to analyze its stability and to reveal the influence of environmental noise and coupling structure on its stability. The main contents of this paper include: 1. By introducing multi-diffusion and white noise into the multi-patch model, the main contents of this paper are as follows: 1. A stochastic multi-patch model with multiple diffusion is established. Combining graph theory with Lyapunov method, the exponential stability criteria of Lyapunov type and coefficient type criterion are obtained. The mean square exponential stability of random coupled oscillators is analyzed by using the coefficient type criterion. The results show that when the topological structure of digraphs satisfies certain conditions and the intensity of white noise is in a certain range, The stochastic model is stable .2. the proportional delay stochastic multi-patch model with multiple diffusion is established. The exponential stability of the model is analyzed, and the Lyapunov type criterion and the coefficient type criterion are obtained. The mean square exponential stability of the proportional delay stochastic coupled oscillator is studied by using the coefficient type criterion. The results show that the exponential stability of the model and the intensity of white noise are obtained. The coefficients of proportional delay are closely related to the topological structure of directed graphs. Combining graph theory and Lyapunov method, the input state stability of stochastic multi-patch model with multiple diffusion is studied, and the sufficient criterion of input state stability is obtained. The input state stability of the stochastic coupled oscillator with input control is studied. The results show that the input state stability of the model is not only related to the input state stability of the vertex system, but also to the input state stability of the vertex system under the appropriate white noise intensity. Combined with the Razumikhin method and graph theory, the stability of coupled neutral stochastic time-delay systems on the network is studied. The Razumikhin type criterion and the coefficient type criterion for moment exponential stability are obtained, and the exponential stability criteria are almost certain. Numerical examples are given to verify the validity of the theoretical results. The results show that the exponential stability of the system depends on the intensity of white noise and the strong connectivity of directed graphs .5.Using Lyapunov method and M-matrix theory, The stochastic stability, stochastic asymptotic stability and global stochastic asymptotic stability of stochastic neural networks with infinite delay and Markov transformation are analyzed. Sufficient conditions for ensuring three stochastic stability of the model are obtained. The results show that when the intensity of white noise is in a certain range, the three stochastic stability of the model is closely related to the generation matrix of the Markov chain.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O175

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