脉冲切换非线性系统的输入—状态稳定性研究

发布时间：2018-12-13 22:38

【摘要】：动力系统是一类由连续时间系统和离散切换信号两部分组成的重要的混杂系统,是当前研究混杂系统方向最热门的重要课题.脉冲系统作为混杂系统重要组成部分,在许多方面都有相当广泛的应用.另外一种重要的组成部分为切换系统,该系统是由一系列的子系统和逻辑规则来协调各个切换.为了更好地研究这类混杂系统,我们把它们结合为一种新的系统,即:脉冲切换系统.输入-状态稳定性由Sontag首次提出,在脉冲切换系统领域很有研究价值,并且推广到非线性系统.输入-状态稳定性意味着无论初始状态是多少,如果输入信号足够小,状态最终会无限小.在本文的研究中,我们引入不稳定子系统,运用多重Lyapunov方法,得出脉冲切换系统的输入-状态稳定性和随机输入-状态稳定性.本文的主要结论可以概括为以下两个部分:1)脉冲切换非线性系统的输入-状态稳定性.在多重Lyapunov函数方法和平均脉冲区间条件下,我们对输入到状态稳定性的研究分三种情况讨论,即:所有子系统稳定,所有子系统不稳定和部分子系统不稳定.如果所有子系统稳定,即使脉冲影响为不稳定脉冲,在有下界的脉冲切换区间条件下,系统仍然为输入-状态稳定.进一步地,如果所有子系统不稳定,在有上界的平均脉冲区间和稳定脉冲影响下,系统仍然为输入-状态稳定.然而,如果存在部分子系统稳定部分子系统不稳定,在特定的条件下,仍然可以证明系统为输入-状态稳定.最后,仿真例子证明了结果的正确性.2)随机脉冲切换非线性系统的随机输入-状态稳定性.研究了一类脉冲切换非线性系统,考虑随机输入-状态稳定性问题.基于Lyapunov函数方法,给出了保证系统随机输入-状态稳定性的充要条件.然后,借助平均脉冲区间技巧,也分三种情况进行讨论.在脉冲影响的作用下,仍然可以证明系统的随机输入-状态稳定性.最后,仿真例子证明了结果的正确性.
[Abstract]:Dynamical system is an important hybrid system which consists of continuous time system and discrete switched signal. As an important part of hybrid system, impulse system is widely used in many fields. Another important component is the handoff system, which is coordinated by a series of subsystems and logic rules. In order to study this kind of hybrid systems better, we combine them into a new system, that is, impulsive switched systems. Input-state stability is proposed by Sontag for the first time. It has great research value in the field of impulsive switched systems and is extended to nonlinear systems. Input-state stability means that no matter what the initial state is, if the input signal is small enough, the state will eventually be infinitely small. In this paper, we introduce the unstable subsystem and obtain the input-state stability and stochastic input-state stability of impulsive switched systems by using the multiplex Lyapunov method. The main conclusions of this paper can be summarized as follows: 1) Input-state stability of impulsive switched nonlinear systems. Under the condition of multiple Lyapunov functions and average impulsive intervals, we discuss the stability of input states in three cases: stability of all subsystems, instability of all subsystems and instability of some subsystems. If all subsystems are stable, even if the pulse effect is unstable, the system is still input-state stable under the condition of lower bound pulse switching interval. Furthermore, if all subsystems are unstable, the system is still input-state stable under the influence of the average pulse interval with upper bound and the stable pulse. However, if some subsystems are stable and some subsystems are unstable, it can still be proved that the system is input-state stable under certain conditions. Finally, a simulation example is given to show the correctness of the results. 2) Stochastic input-state stability of stochastic impulsive switched nonlinear systems. In this paper, a class of impulsive switched nonlinear systems is studied. The problem of stochastic input-state stability is considered. Based on the Lyapunov function method, a necessary and sufficient condition is given to guarantee the stochastic input-state stability of the system. Then, with the help of the average pulse interval technique, it is also discussed in three cases. The stochastic input-state stability of the system can still be proved under the influence of impulses. Finally, a simulation example is given to show the correctness of the results.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19

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