切换正系统的镇定设计

发布时间：2018-10-09 18:00

【摘要】：正系统是一类在现实中很常见的系统,比如:人口模型、经济发展模式等等。它是一类当初始条件和输入为非负值时,系统的状态和输出始终为非负值的动态系统。切换系统作为一种不可或缺的混合系统,在机房管理、交通系统、电力系统等有很好的应用。它是由子系统和切换规则组成。切换正系统是由有限个正子系统和切换信号组成的一类系统。在过去十年里,切换正系统在通信、医疗、自动化等范围内吸引了愈来愈多研究者的注意力。按照切换正系统在不同应用中发挥的作用来看,它要符合两点性质,正的且具有切换律。应当指出:切换正系统在很多问题的研究上与上述两种系统相比具有很大的挑战性。论文从以下几个方面展开研究:第一章是绪论。论述了切换正系统的研究意义,总结了切换正系统研究的一些主要问题及现状。结合切换正系统的一些理论问题,如:稳定、镇定、观测等。根据这些问题介绍了解决切换正系统问题所需要的方法和工具。最后,介绍了本文的主要内容和框架。第二章探讨了多胞体切换正系统的鲁棒镇定问题。首先,利用多线性余正Lyapunov函数方法,探讨了多胞体切换正系统的镇定问题。其次,借助线性规划方法,给出多胞体切换正系统全局指数稳定的充分条件,设计出状态反馈控制律,解决了多胞体切换正系统的镇定问题。本章最后给出的仿真案例声明了提出方法的有效性。第三章研究了改进的切换正系统的镇定问题。利用矩阵分解方法,设计出新的控制器,构造出新的系统反馈控制律,使增益矩阵的秩不再局限为1,降低了结论的保守性。同时,使得给出的系统既是正的又是稳定的。最后,通过仿真验证了提出方法的有效性。第四章考虑了切换正系统具有l_1增益的镇定设计。利用多线性余正Lyapunov函数,建立了使系统基于平均驻留时间上镇定的充分条件。同时,给出了使系统镇定的反馈控制律,得到了L_1增益。最后,举例检验给出方法的可行性。第五章是总结与展望。首先,总结了本文的重要结论。其次,提出了今后可能进行研究的问题。
[Abstract]:Positive system is a kind of system that is very common in reality, such as population model, economic development model and so on. It is a kind of dynamic system whose state and output are always non-negative when the initial condition and input are non-negative. As an indispensable hybrid system, switching system has a good application in computer room management, traffic system, power system and so on. It consists of subsystems and switching rules. Switched positive system is a class of systems composed of finite positive subsystems and switched signals. In the past decade, switching forward systems have attracted more and more researchers' attention in the fields of communication, medicine, automation and so on. According to the function of switched positive system in different applications, it should conform to two-point property, positive and have switching law. It should be pointed out that switched forward systems are more challenging than these two systems in many problems. The thesis starts the research from the following aspects: the first chapter is the introduction. This paper discusses the significance of the research of switched forward system, and summarizes some main problems and present situation of the research of switched forward system. Combined with some theoretical problems of switched positive systems, such as stability, stabilization, observation and so on. According to these problems, the methods and tools needed to solve the problem of switching forward system are introduced. Finally, the main contents and framework of this paper are introduced. In chapter 2, the problem of robust stabilization for multibody switched positive systems is discussed. Firstly, the stabilization problem of multi-cell body switching positive systems is discussed by using the method of multi-linear copositive Lyapunov function. Secondly, by means of linear programming, sufficient conditions for the global exponential stability of the positive system with multiple cell bodies switching are given, and the state feedback control law is designed to solve the stabilization problem of the positive system with multiple cell body switching. At the end of this chapter, a simulation case is given to illustrate the effectiveness of the proposed method. In chapter 3, we study the stabilization of improved switched forward systems. By using matrix decomposition method, a new controller is designed and a new feedback control law is constructed. The rank of the gain matrix is no longer limited to 1, which reduces the conservatism of the conclusion. At the same time, the given system is both positive and stable. Finally, the effectiveness of the proposed method is verified by simulation. In chapter 4, we consider the stabilization design of switched positive systems with L _ S _ 1 gain. By using the multilinear copositive Lyapunov function, a sufficient condition is established to stabilize the system based on the average dwell time. At the same time, the feedback control law of stabilizing the system is given, and the L _ S _ 1 gain is obtained. Finally, the feasibility of the method is verified by examples. The fifth chapter is the summary and prospect. Firstly, the important conclusions of this paper are summarized. Secondly, the possible problems in the future are put forward.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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