正Markov跳变线性系统的随机有限时间控制与滤波

发布时间：2018-04-30 19:21

本文选题：正Markov跳变线性系统 + 随机有限时间有界性　；参考：《山东大学》2017年硕士论文

【摘要】：有限时间有界性是指系统在给定有界的初始条件和有界的外部扰动情形下,系统的状态在一段固定的有限时间区间内总是不超过某一给定的阈值.本文研究了正Markov跳变线性系统的随机有限时间控制及滤波问题,分别在离散时间和连续时间情形下对正Markov跳变线性系统的随机有限时间有界性分析,控制器设计,性能分析及正滤波器设计进行了讨论.第一章是本文的研究背景.本章系统地阐述了正Markov跳变线性系统和有限时间控制的研究背景和已有结果,指出了正Markov跳变线性系统随机有限时间控制和滤波领域存在的问题,并介绍了本文的主要工作,最后给出了文中用到的数学符号的说明.第二章讨论了离散时间情形下正Markov跳变线性系统的随机有限时间控制及滤波问题.第一部分将有限时间有界性的概念扩展到离散时间正Markov跳变线性系统,通过引入示性函数,将正Markov跳变线性系统的随机有限时间有界性分析问题转换为相应的增广系统的有限时间有界性分析问题,得出正Markov跳变线性系统随机有限时间有界的线性规划形式的充分条件,并在此基础上设计了有限时间控制器;第二部分通过分析增广系统的有限时间l1增益性能,得到了正Markov跳变线性系统的有限时间l1增益性能的充分条件,通过求解标准的线性规划问题给出了有限时间正l1增益滤波器的设计方法.第三章讨论了连续时间情形下正Markov跳变线性系统的随机有限时间控制及滤波问题.通过建立连续时间正Markov跳变线性系统的随机有限时间有界性和L1增益性能与增广的确定性连续时间线性正系统的有限时间有界性和L1增益性能的等价关系,得到了正Markov跳变线性系统的随机有限时间有界性和有限时间L1增益性能的充分条件,进而设计了有限时间控制器和有限时间正L1增益滤波器.
[Abstract]:Finite time boundedness means that the state of the system is always within a given threshold in a given bounded initial condition and bounded external disturbance. In this paper, the stochastic finite time control and filtering problem for positive Markov jump linear systems are studied. The stochastic finite time boundedness analysis and controller design for positive Markov jump linear systems with discrete time and continuous time respectively are studied. Performance analysis and positive filter design are discussed. The first chapter is the background of this paper. In this chapter, the research background and existing results of positive Markov jump linear systems and finite time control are systematically described. The problems in the field of stochastic finite time control and filtering for positive Markov jump linear systems are pointed out, and the main work of this paper is introduced. Finally, the mathematical symbols used in this paper are explained. In chapter 2, stochastic finite time control and filtering for linear systems with positive Markov jump are discussed. In the first part, the concept of finite time boundedness is extended to discrete-time positive Markov jump linear systems. In this paper, the stochastic finite time boundedness analysis problem of positive Markov jump linear systems is transformed into the finite time boundedness analysis problem of the corresponding augmented systems, and the sufficient conditions for the bounded stochastic finite time linear programming of positive Markov jump linear systems are obtained. Based on this, a finite time controller is designed. In the second part, by analyzing the finite time L1 gain performance of the augmented system, the sufficient conditions for the finite time L1 gain performance of the positive Markov jump linear system are obtained. By solving the standard linear programming problem, the design method of finite time positive L1 gain filter is presented. In chapter 3, stochastic finite time control and filtering for linear systems with positive Markov jump are discussed. By establishing the boundedness of stochastic finite time and the equivalence of L1 gain performance with the finite time boundedness and L1 gain performance of the extended deterministic continuous-time linear linear system with positive Markov jump, The boundedness of stochastic finite time and sufficient conditions of gain performance of finite time L1 for positive Markov jump linear systems are obtained. Furthermore, a finite time controller and a finite time positive L1 gain filter are designed.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13;TN713

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