状态脉冲控制系统的脉动现象及稳定性研究
发布时间：2018-08-01 11:04
【摘要】：脉冲系统是描述事物在其发展过程中受到扰动而引起瞬时突变现象的一类数学模型.随着科学技术的突飞猛进,脉冲系统理论的重要性及其在实践中的应用价值日益凸显.而实际问题一般是存在脉动现象的复杂系统,因此,如何控制状态脉冲系统的脉动现象是否发生具有重要的现实意义.基于脉冲系统理论发展起来的脉冲控制系统,由于它的控制实现简单、成本低、反应快、能耗小而得到广泛的应用.稳定性是这些系统的首要特性.因此,脉冲控制系统的稳定性的研究成为当今国际控制界的热门问题.本文主要讨论了状态脉冲控制系统的脉动现象及稳定性问题.全文的主要研究工作包括:在第一章中,主要介绍了本文的研究背景、意义和已有的一些研究成果.在第二章中,研究了状态脉冲系统的脉动现象,建立了保证状态脉冲系统的脉动现象发生与否的一些充分条件,推广并改进了原有的结果,并给出了两个例子说明所得结果的有效性.在第三章中,利用线性分解的方法,建立了保证状态脉冲控制系统渐近稳定和指数稳定的一些充分条件,并给出一个例子说明所得结果的优越性.在第四章中,通过建立退化系统及拟稳定的概念,将状态脉冲时滞系统的非平凡解的稳定性问题转化为具固定时刻的时滞系统的平凡解的稳定性问题.利用具固定时刻脉冲时滞系统已有的稳定性结果,得到状态脉冲时滞系统的非平凡解的一些拟稳定性结果.
[Abstract]:Pulse system is a kind of mathematical model that describes the instantaneous catastrophe caused by disturbance in the course of its development. With the rapid progress of science and technology, the importance of the theory of pulse system and its application in practice are increasingly prominent. The actual problem is generally a complex system with pulse phenomenon, so how to control it The pulsating phenomenon of the state pulse system has an important practical significance. The pulse control system based on the theory of pulse system has been widely used because of its simple control, low cost, fast reaction and low energy consumption. Stability is the primary characteristic of these systems. Therefore, the stability of these systems is studied. This paper mainly discusses the pulsation and stability of state pulse control system. The main research work of this paper is as follows: in the first chapter, the research background, significance and some existing research results are mainly introduced. In the second chapter, the pulsation of state pulse system is studied. Some sufficient conditions for the occurrence of pulsating phenomenon of state pulse system are established, and the original results are extended and improved. Two examples are given to illustrate the validity of the results. In the third chapter, the asymptotic stability and exponential stability of the state pulse control system are established by using the linear decomposition method. In the fourth chapter, in the fourth chapter, the stability of the nontrivial solution of a state pulse delay system is converted to the stability of a time-delay system with fixed time by establishing the degenerate system and the quasi stable concept. Some stability results are obtained, and some quasi stability results for nontrivial solutions of state impulsive delayed systems are obtained.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2157367
[Abstract]:Pulse system is a kind of mathematical model that describes the instantaneous catastrophe caused by disturbance in the course of its development. With the rapid progress of science and technology, the importance of the theory of pulse system and its application in practice are increasingly prominent. The actual problem is generally a complex system with pulse phenomenon, so how to control it The pulsating phenomenon of the state pulse system has an important practical significance. The pulse control system based on the theory of pulse system has been widely used because of its simple control, low cost, fast reaction and low energy consumption. Stability is the primary characteristic of these systems. Therefore, the stability of these systems is studied. This paper mainly discusses the pulsation and stability of state pulse control system. The main research work of this paper is as follows: in the first chapter, the research background, significance and some existing research results are mainly introduced. In the second chapter, the pulsation of state pulse system is studied. Some sufficient conditions for the occurrence of pulsating phenomenon of state pulse system are established, and the original results are extended and improved. Two examples are given to illustrate the validity of the results. In the third chapter, the asymptotic stability and exponential stability of the state pulse control system are established by using the linear decomposition method. In the fourth chapter, in the fourth chapter, the stability of the nontrivial solution of a state pulse delay system is converted to the stability of a time-delay system with fixed time by establishing the degenerate system and the quasi stable concept. Some stability results are obtained, and some quasi stability results for nontrivial solutions of state impulsive delayed systems are obtained.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前1条
1 綦建刚,吕永敬,靳明忠;脉冲微分方程的脉冲聚点存在的一般性条件[J];数学物理学报;2001年03期
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