基于离散化Lyapunov-Krasovskii泛函方法的时滞Markov跳变系统分析与综合

Markov jump systems with time delays are a class of stochastic hybrid systems with complex structure, which have a broad application prospect. The discretized Lyapunov-Krasovskii functional method has great potential for reducing the conservatism of the existing analysis and synthesis results. This project is concerned with the stochastic stability and memory feedback H∞ problems of the Markov jump systems with mode-dependent time delays. The research plan is as follows: first, use the discretized Lyapunov-Krasovskii functional method to discuss the stochastic stability problem of the systems for developing some less conservative and easily verified delay-dependent criteria; then, establish effective control strategies for the memory state-feedback and memory output-feedback H∞ control problems; next, investigate the computational complexity problems of the obtained results for finding effective ways to improve the calculating efficiency; last, make an active effort to explore the application of theoretical results to the maneuvering target tracking area. The successful implementation of this project will further enrich and develop the control theory of Markov jump systems with time delays, and provide significant reference for their engineering applications as well.

时滞Markov跳变系统是一类结构复杂的随机混杂系统，具有广泛的应用前景。离散化Lyapunov-Krasovskii泛函方法在降低现有分析与综合结果的保守性方面具有较大潜力。本项目拟以具有模态依赖时滞的Markov跳变系统为研究对象，按以下思路对其随机稳定性问题和有记忆反馈H∞控制问题开展深入的研究。首先，运用离散化Lyapunov-Krasovskii泛函方法研究这类系统的随机稳定性问题，旨在获得一些较少保守、易于验证的时滞相关判据。然后，探究系统的有记忆状态反馈、有记忆输出反馈H∞控制问题，提出行之有效的控制策略。在此基础上，讨论所得分析与设计结果的计算复杂度问题，给出提高计算效率的有效途径。最后，对所得理论结果在机动目标跟踪这一领域的应用进行积极的探索。本项目的实施，将进一步丰富和发展时滞Markov跳变系统的控制理论，并对其工程实践提供新的参考依据。

Markov跳变系统由多个子系统和一个离散状态的Markov过程构成，系统状态依据这个Markov过程在各个子系统间进行切换。在工程领域，零部件随机故障、突发性环境扰动、子系统互联变动等事件容易导致一些实际系统在结构或参数上产生突变。对这些系统而言，其状态演化可视为由时间和事件共同驱动。Markov跳变系统的理论与方法在对这些系统的定性描述、性能分析与控制设计方面，展现了良好的应用前景。本项目应用随机分析理论、Lyapunov方法、以及一些不等式技巧，对时滞Markov跳变神经网络系统的驱动-响应混沌同步、Markov跳变拓扑多智能体系统的H∞/L2-L∞一致性、离散时间随机分布时滞Markov跳变系统的异步耗散滤波、模型信息部分可用非线性Markov跳变系统的有限时间l2-l∞跟踪、基于Markov跳变模型的T-S模糊时滞系统可靠混合H∞/无源控制、奇异摄动Semi-Markov跳变系统的慢状态变量反馈镇定等问题进行了具体研究，获得了一些较少保守的均方稳定性判据，给出了易于实现的控制器/滤波器设计策略，并通过数值仿真示例对所得分析、设计结果的有效性进行了验证。