【摘要】：脈沖系統(tǒng)是描述事物在其發(fā)展過程中受到擾動(dòng)而引起瞬時(shí)突變現(xiàn)象的一類數(shù)學(xué)模型.隨著科學(xué)技術(shù)的突飛猛進(jìn),脈沖系統(tǒng)理論的重要性及其在實(shí)踐中的應(yīng)用價(jià)值日益凸顯.而實(shí)際問題一般是存在脈動(dòng)現(xiàn)象的復(fù)雜系統(tǒng),因此,如何控制狀態(tài)脈沖系統(tǒng)的脈動(dòng)現(xiàn)象是否發(fā)生具有重要的現(xiàn)實(shí)意義.基于脈沖系統(tǒng)理論發(fā)展起來的脈沖控制系統(tǒng),由于它的控制實(shí)現(xiàn)簡單、成本低、反應(yīng)快、能耗小而得到廣泛的應(yīng)用.穩(wěn)定性是這些系統(tǒng)的首要特性.因此,脈沖控制系統(tǒng)的穩(wěn)定性的研究成為當(dāng)今國際控制界的熱門問題.本文主要討論了狀態(tài)脈沖控制系統(tǒng)的脈動(dòng)現(xiàn)象及穩(wěn)定性問題.全文的主要研究工作包括:在第一章中,主要介紹了本文的研究背景、意義和已有的一些研究成果.在第二章中,研究了狀態(tài)脈沖系統(tǒng)的脈動(dòng)現(xiàn)象,建立了保證狀態(tài)脈沖系統(tǒng)的脈動(dòng)現(xiàn)象發(fā)生與否的一些充分條件,推廣并改進(jìn)了原有的結(jié)果,并給出了兩個(gè)例子說明所得結(jié)果的有效性.在第三章中,利用線性分解的方法,建立了保證狀態(tài)脈沖控制系統(tǒng)漸近穩(wěn)定和指數(shù)穩(wěn)定的一些充分條件,并給出一個(gè)例子說明所得結(jié)果的優(yōu)越性.在第四章中,通過建立退化系統(tǒng)及擬穩(wěn)定的概念,將狀態(tài)脈沖時(shí)滯系統(tǒng)的非平凡解的穩(wěn)定性問題轉(zhuǎn)化為具固定時(shí)刻的時(shí)滯系統(tǒng)的平凡解的穩(wěn)定性問題.利用具固定時(shí)刻脈沖時(shí)滯系統(tǒng)已有的穩(wěn)定性結(jié)果,得到狀態(tài)脈沖時(shí)滯系統(tǒng)的非平凡解的一些擬穩(wěn)定性結(jié)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.
【學(xué)位授予單位】：山東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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相關(guān)期刊論文 前1條

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本文編號(hào)：2157367