状态切换的随机时滞系统的稳定性分析与控制及应用

项目名称： 状态切换的随机时滞系统的稳定性分析与控制及应用

项目编号： No.61503046

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 宋银芳

作者单位： 长江大学

项目金额： 20万元

中文摘要： 近二十多年来，随机切换系统受到了人们的广泛关注，并获得了丰富的成果，已有的工作主要集中于Markov调制及时间切换的随机时滞系统，而依赖于状态切换的随机时滞系统的稳定性与控制问题的研究成果并不多. 因此本项目首先研究依赖于状态切换的随机时滞系统的稳定性: 当各子系统满足线性增长条件时，建立该系统的Razumikhin定理，以探讨其矩指数稳定性；当各子系统满足非线性增长条件时讨论其全局解的存在唯一性，建立该系统的LaSalle不变原理; 再进一步分析其随机输入状态稳定性. 随后考虑其控制问题，一方面设计合适的切换律与反馈控制律，使系统指数镇定；另一方面分析其耗散性与无源性. 最后研究一类特殊状态切换的随机时滞系统，即随机忆阻神经网络系统的矩稳定性、耗散性与无源性及同步控制问题. 以上工作不仅将丰富和发展随机动力学理论，而且为忆阻器在人工智能方面的应用提供必要的依据.

中文关键词： 状态切换；随机时滞系统；稳定性；反馈控制；忆阻神经网络系统

英文摘要： Stochastic switched systems have been received considerable attention during the past few decades and abundant research achievements have been obtained. However, the existed results mainly focused on the stochastic systems with Markov switching and time switching. As far as we know, stability analysis and control of stochastic delay-time systems with state-dependent switching haven't been considered. Therefore, this issue aims to this case. When every subsystem of the underlying system satisfies the linear growth condition, we firstly establish Ruzumikhin theorem to examine the moment exponential stability. If every subsystem satisfies the polynomial growth condition, we discuss the existence and uniqueness of global solution and attempt to give the LaSalle theorem. Moreover, stochastic input-to-state stability is introduced and analyzed. Secondly, we investigate the problem of stochastic control. Concretely, on one hand we design the appropriate switching rule and feedback controllers to guarantee the exponential stabilization. On the other hand, we analyze dissipativeness and passivity of stochastic systems. Finally, we investigate the moment stability, dissipativeness, passivity and synchronization control of stochastic memristor-based neural networks with time delays. Our work not only will enrich and develop stochastic dynamic theory, buy also provide the theoretic foundation for application of memristor to artificial intelligence.

英文关键词： state-dependent switching;stochastic delay-time systems;stability;feedback control;memristor-based neural networks