离散切换正系统的稳定性与镇定性

发布时间：2018-03-16 03:30

本文选题：指数稳定　切入点：有限时间稳定　出处：《陕西师范大学》2016年博士论文　论文类型：学位论文

【摘要】：本文主要研究离散切换正系统的稳定性与镇定性.首先,本文研究了离散切换正系统的指数稳定和镇定问题.其次,当控制器的切换时刻滞后于对应子系统的切换时刻时,本文进一步研究了离散切换正系统的异步镇定和异步有限时间控制.最后,本文也进一步讨论了离散正奇异时滞系统的指数稳定和离散切换正奇异系统的有限时间稳定等问题.主要内容如下:第一章介绍了切换系统,切换正系统,Lyapunov稳定及有限时间稳定的基本知识.为了给出离散正奇异系统的解,进一步介绍了广义逆的相关理论.第二章研究了离散切换正系统的稳定性和镇定性问题.首先,通过构造多线性协正Lyapunov函数,利用前向模型依赖平均驻留时间切换信号,得到了离散切换正系统指数稳定的一个充分条件.并指出,当切换信号满足一定的假设条件时,前面文献中的一些结果可以看作是该结果的一个推论.其次,基于多采样类-Lyapunov函数差分的方法,得到了线性离散切换正系统指数稳定的另一个充分条件.根据所得结论,设计了一类模型依赖状态反馈控制器使得闭环系统在前向模型依赖平均驻留时间切换信号下是正的且是指数稳定的.最后,给出了两个数值例子说明了所得理论结果的正确性.第三章讨论了含有时变时滞的离散切换正系统的异步镇定性.首先,通过构造适当的Lyapunov-Krasovskii泛函,得到了离散切换正时滞系统在模型依赖平均驻留时间切换信号下指数稳定的一个充分条件.其次,通过允许所选择的Lyapunov-Krasovskii泛函在被激活的子系统和控制器不匹配的时间区间内递增,基于模型依赖平均驻留时间切换信号,得到了存在一类状态反馈控制器使得闭环系统在异步切换下是正的且是指数稳定的充分条件.最后,给出两个数值例子说明了所提出方法的有效性.第四章讨论了离散脉冲切换正时滞系统在异步切换下的有限时间控制.首先,通过构造一个适当的Lyapunov函数,得到了离散脉冲切换正时滞系统在模型依赖平均驻留时间切换信号下有限时间稳定的一个充分条件.其次,通过构造另一个不同的Lyapunov函数,得到了存在一类状态反馈控制器使得闭环系统在异步切换下是正的且是有限时间稳定的几个充分条件,并给出了控制器增益的具体形式.最后,给了一个数值例子说明了所得结果的有效性和可行性.第五章研究了离散正奇异时滞系统的指数稳定性.首先,利用奇异值分解和单模坐标变换,得到了离散奇异时滞系统是正的一个充要条件.其次,通过构造适当的线性协正Lyapunov函数,得到了离散正奇异时滞系统指数稳定的一个充分条件.并且,所得到的结果都是以代数矩阵不等式的形式给出的,它们可以利用Matlab中的线性规划工具箱数值的进行求解.最后,给出了一个数值例子说明了所提出方法的有效性.第六章讨论了离散切换正奇异系统的有限时间稳定问题.首先,提出了离散切换正奇异系统有限时间稳定的概念,并给出了一个假设条件保证离散切换正奇异系统具有相容切换.其次,利用状态转移矩阵,得到了当离散切换正奇异系统具有相容切换时,其在任意切换下有限时间稳定的充要条件.进一步,通过构造拟线性Lyapunov函数,基于模型依赖平均驻留时间切换信号,以代数矩阵不等式的形式给出了离散切换正奇异系统在相容切换下有限时间稳定的另一个充分条件.最后,给出了一个数值例子表明了所提出方法的有效性.
[Abstract]:This paper mainly studies the stability and the town of discrete-time switched positive systems qualitatively. Firstly, in this paper the discrete switched positive systems exponential stability and stabilization problem. Secondly, when the time of the switching controller switching time lag in the corresponding subsystem, this paper further studies the discrete switching stabilization system is asynchronous and asynchronous finite time control. Finally, this paper also further discusses the discrete singular time-delay systems and exponential stability of discrete switched singular systems are finite time stability problems. The main contents are as follows: the first chapter introduces the switching system, switching system, the basic knowledge of Lyapunov stability and finite time stability of discrete singular system is given. In order to further introduce solutions. The theory of generalized inverse. The second chapter studies the stability and stabilization of discrete-time switched positive systems. Firstly, by constructing multiple linear copositive Lyapu The Nov function, the forward model depends on average dwell time switching signal, a sufficient condition is obtained for the exponential stability of discrete-time switched positive systems. And pointed out that when the switching signal satisfies certain assumptions, some in front of the results in the literature can be seen as a corollary of this result. Secondly, multi class -Lyapunov function difference based method, another sufficient condition is obtained for linear discrete-time switched system is exponentially stable. According to the conclusion, design a kind of model dependent state feedback controller such that the closed-loop system in the forward model depend on average dwell time switching signal is positive and is exponentially stable. Finally, two numerical example is given to illustrate the correctness of the theoretical results. The third chapter discusses the asynchronous stabilization of discrete-time switched positive systems with time-varying delay. Firstly, by constructing appropriate Lyapunov-Kraso The vskii function, obtained discrete switched systems with time delay is dependent on a sufficient condition of average dwell time switching exponential stability in the model. Secondly, by allowing the choice of Lyapunov-Krasovskii functional mismatch in the sub system and the controller is activated by the time interval increases, the model depends on average dwell time switching signals are obtained based on the a state feedback controller such that the closed-loop system under asynchronous switching is positive and the sufficient conditions of exponential stability. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method. The fourth chapter discusses the discrete pulse finite time under asynchronous switching control is switched delay systems. Firstly, by constructing a the appropriate Lyapunov function, the Discrete Impulsive Switched Systems with time delay is dependent on the average dwell time switching signal in a finite time stability model A sufficient condition. Secondly, by constructing a different Lyapunov function, the existence of a state feedback controller such that the closed-loop system under asynchronous switching is positive and some sufficient conditions for finite time stability, and gives the specific form of controller gain. The most effective, gave a numerical example to illustrate the obtained results and feasibility. The fifth chapter studies the exponential stability of discrete singular time-delay systems. Firstly, by using singular value decomposition and single mode coordinate transformation, the discrete singular time-delay systems is a necessary and sufficient condition is. Secondly, through linear co constructing Lyapunov function, a sufficient condition is given index of discrete singular time-delay systems is stable. And the results are given in the form of algebraic matrix inequality, they can use the linear programming tool box in Matlab number The values are solved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. The sixth chapter discusses the finite time discrete switched singular systems are stable. First, put forward the concept of discrete switching is singular finite time stability of the system, and gives an assumption to guarantee the discrete-time switched positive singular the system has compatibility switch. Secondly, using the state transition matrix is obtained when the discrete singular systems with switching are compatible when switching, the necessary and sufficient conditions for finite time stability under arbitrary switching. Further, by constructing a quasi linear Lyapunov function model depends on average dwell time switching signal based on the given by the discrete algebraic matrix inequalities switching is singular system in another sufficient condition of finite time stability compatible switching. Finally, a numerical example is given to show that the proposed method Effectiveness.

【学位授予单位】：陕西师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O231

【参考文献】