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

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

项目编号： No.61503002

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： 周建平

作者单位： 安徽工业大学

项目金额： 20万元

中文摘要： 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。

中文关键词： Markov跳变系统；随机混杂系统；时滞相关判据；H无穷控制；离散化Lyapunov-Krasovskii泛函

英文摘要： 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.

英文关键词： Markov Jumping System;Stochastic Hybrid System;Delay-Dependent Criterion;H∞ Control;Discretized Lyapunov-Krasovskii Functional