脉冲切换系统有限时间圆环域稳定性研究

发布时间：2018-09-01 09:12

【摘要】：脉冲切换系统是一类重要的混杂系统,最近几年,由于其在自动化控制,计算机控制,过程控制等领域的广泛应用而受到了人们的关注.迄今为止,关于脉冲系统和切换系统有限时间稳定性问题的研究已有了很多相关结论,但是关于脉冲切换系统的有限时间稳定性问题的结果非常少,并且主要集中在最近几年;关于系统有限时间圆环域稳定性的研究更是少之又少.因此,对于脉冲切换系统的有限时间圆环域稳定性的研究具有重要的价值.基于以上的讨论,本文我们主要来研究下面两种不同类型的脉冲切换系统的有限时间圆环域稳定性问题,具体内容和研究成果如下:第一部分我们采用模态依赖于参数和平均脉冲时间相结合的方法研究了一类脉冲切换系统的有限时间圆环域稳定性问题.本部分主要贡献为:首先,我们把有限时间圆环域稳定的概念推广到脉冲切换系统,然后定义了平均脉冲区间,给出脉冲切换系统有限时间圆环域稳定的充分条件,并分析不同的脉冲强度对系统稳定性的影响.虽然不同的脉冲强度对系统的影响是不同的,但是,我们在不要求脉冲切换区间的上下界,仍能保证系统都是有限时间圆环域稳定的.第二部分我们仍然采用模态依赖于参数和平均脉冲时间相结合的方法,研究了随机脉冲系统在异步Markovian切换下的有限时间圆环域稳定性问题.首先,我们以一个定理形式给出了非线性随机Markovian异步脉冲切换系统在异步段不稳定,同步段稳定的情况下,有限时间圆环域稳定所需的条件.并且我们将这一结果推广到了线性随机Markovian异步脉冲切换系统中.进一步地,我们研究了非线性系统在同步段和异步段都不稳定的情况下的有限时间圆环域稳定性问题.这一种情况更加复杂一些,因此所需的条件也就更加严格一些,但仍是可以实现的.与此同时,我们也将结果推广到了线性随机Markovian异步脉冲切换系统中去.
[Abstract]:Impulse switching system is an important hybrid system. In recent years, it has been widely used in the fields of automation control, computer control, process control and so on. Up to now, there have been many related conclusions on the finite time stability of impulsive systems and switched systems, but the results on the finite time stability of impulsive switched systems are very few, and they are mainly focused in recent years. There are few researches on the stability of the system in finite time domain. Therefore, it is of great value to study the stability of impulsive switched systems in finite time annular domain. Based on the above discussion, we mainly study the following two kinds of impulsive switched systems in finite time ring domain stability. The main contents and results are as follows: in the first part, we study the stability of a class of impulsive switched systems in finite time annular domain by means of the combination of modal dependent parameters and average impulsive time. The main contributions of this part are as follows: firstly, we extend the concept of finite time ring domain stability to impulsive switched systems, then define the mean impulsive interval, and give the sufficient conditions for the finite time ring domain stability of impulsive switched systems. The influence of different pulse intensity on the stability of the system is analyzed. Although the influence of different pulse intensity on the system is different, we can ensure that the system is stable in the circle domain of finite time without requiring the upper and lower bounds of the pulse switching interval. In the second part, we still study the stability of stochastic impulsive systems in finite time annular domain under asynchronous Markovian switching using the combination of modal dependent parameters and average pulse time. Firstly, in the form of a theorem, we give the necessary conditions for the stability of a nonlinear stochastic Markovian asynchronous pulse switching system in the case of unstable asynchronous segment and stable synchronous segment. And we extend this result to linear stochastic Markovian asynchronous impulsive switched systems. Furthermore, we study the stability of a finite time ring in the case of instability in both synchronous and asynchronous segments of nonlinear systems. This situation is more complex, so the conditions are more stringent, but still achievable. At the same time, we extend the results to linear stochastic Markovian asynchronous impulsive switching systems.
【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】：O175

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