本文關(guān)鍵詞： 分布式時(shí)滯系統(tǒng) 中立型時(shí)滯系統(tǒng) Lyapunov-Krasovskii泛函 線性矩陣不等式　出處：《青島大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：實(shí)際系統(tǒng)中時(shí)滯因素的存在嚴(yán)重影響著系統(tǒng)的動(dòng)態(tài)行為。多年來,對(duì)時(shí)滯系統(tǒng)穩(wěn)定性的研究一直是系統(tǒng)理論領(lǐng)域的重要課題,也受到社會(huì)各界學(xué)者的廣泛關(guān)注。本文應(yīng)用李雅普諾夫穩(wěn)定性理論,對(duì)兩類時(shí)滯系統(tǒng)進(jìn)行穩(wěn)定性分析,得到了判定系統(tǒng)穩(wěn)定的充分條件。本文主要的工作是:首先,應(yīng)用自由權(quán)矩陣技術(shù)及矩陣不等式方法,得到一個(gè)改進(jìn)型的二重積分不等式。與Wirtinger型二重積分不等式對(duì)比發(fā)現(xiàn),在理論和實(shí)際應(yīng)用中均能使系統(tǒng)的保守性降低。其次,分析分布式時(shí)滯系統(tǒng)和中立型時(shí)滯系統(tǒng)的穩(wěn)定性。構(gòu)造恰當(dāng)?shù)腖yapunov-Krasovskii函數(shù)并應(yīng)用該改進(jìn)型不等式,得到了新的判定這兩類系統(tǒng)穩(wěn)定的充分條件,并列舉數(shù)值例子進(jìn)行對(duì)比。仿真結(jié)果表明,本文得到的最大時(shí)滯上界值均大于以往文獻(xiàn)的值,說明應(yīng)用本文提出的不等式方法能有效地降低系統(tǒng)的保守性。本文的研究內(nèi)容對(duì)提高系統(tǒng)穩(wěn)定性分析方法具有重要意義。最后,對(duì)兩類時(shí)滯系統(tǒng)的穩(wěn)定性分析過程歸納、總結(jié),針對(duì)已有的理論成果,提出了今后研究工作的規(guī)劃和設(shè)想。
[Abstract]:The existence of time-delay factors in practical systems seriously affects the dynamic behavior of systems. For many years, the study of the stability of time-delay systems has been an important topic in the field of system theory. This paper applies Lyapunov stability theory to analyze the stability of two kinds of time-delay systems. The main work of this paper is as follows: firstly, the free matrix technique and matrix inequality method are used. A modified double integral inequality is obtained. Compared with the Wirtinger type double integral inequality, it is found that the conservatism of the system can be reduced both in theory and in practice. The stability of distributed time-delay systems and neutral time-delay systems is analyzed. The appropriate Lyapunov-Krasovskii function is constructed and the improved inequality is applied. A new sufficient condition for judging the stability of these two systems is obtained, and numerical examples are given to compare them. The simulation results show that the maximum delay upper bound values obtained in this paper are higher than those in previous literatures. It shows that the inequality method proposed in this paper can effectively reduce the conservatism of the system. The research content of this paper is of great significance to improve the stability analysis method of the system. Finally. The process of stability analysis for two classes of time-delay systems is summarized. According to the existing theoretical results, the planning and assumption of the future research work are put forward.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

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本文編號(hào)：1480834