發(fā)布時(shí)間：2018-04-25 13:08

  本文選題：泊松跳躍 + 算子譜��； 參考：《山東科技大學(xué)》2017年碩士論文

【摘要】：帶泊松跳躍的隨機(jī)系統(tǒng)可以更好的描述系統(tǒng)外突然發(fā)生的隨機(jī)擾動(dòng),近年來越來越多的學(xué)者開始關(guān)注這個(gè)領(lǐng)域。帶泊松跳隨機(jī)系統(tǒng)在物理、化學(xué)、工程、金融、生物系統(tǒng)等領(lǐng)域有著重要應(yīng)用,研究帶泊松跳隨機(jī)系統(tǒng)有著重要意義。本文主要研究了由泊松跳躍和布朗運(yùn)動(dòng)共同驅(qū)動(dòng)的線性隨機(jī)系統(tǒng)的穩(wěn)定性與能觀測(cè)性。主要成果如下:利用譜分析方法得到系統(tǒng)漸近均方穩(wěn)定的充分必要條件。將“不可移動(dòng)的譜”的概念推廣到帶泊松跳線性隨機(jī)系統(tǒng)的基礎(chǔ)上,并得到“不可移動(dòng)的譜”的判別定理。用“不可移動(dòng)的譜”為工具給出了系統(tǒng)可否鎮(zhèn)定的判別定理。在使用算子譜定義區(qū)間穩(wěn)定的基礎(chǔ)上研究了線性隨機(jī)系統(tǒng)的區(qū)間穩(wěn)定性并得到了系統(tǒng)狀態(tài)收斂速度與區(qū)間(-β,-α)的關(guān)系。使用線性矩陣不等式和Schur補(bǔ)引理得到系統(tǒng)區(qū)間穩(wěn)定的判別定理。在定義精確能觀測(cè)和精確能檢測(cè)的基礎(chǔ)上得到相應(yīng)的判別定理。在此基礎(chǔ)上分析了系統(tǒng)穩(wěn)定、精確能觀測(cè)、精確能檢測(cè)以及廣義李雅普諾夫不等式之間的關(guān)系。同時(shí),為了方便理解本文在一些章節(jié)中給出了數(shù)值算例。
[Abstract]:Random systems with Poisson hops can better describe the sudden random disturbance outside the system. In recent years, more and more scholars have begun to pay attention to this field. The stochastic systems with Poisson jump have important applications in the fields of physics, chemistry, engineering, finance, biological systems and other fields. This paper is important to study the random system with Poisson jump. The stability and observability of a linear stochastic system driven by a Poisson jump and Brown motion are studied. The main results are as follows: the necessary and sufficient conditions for the asymptotic mean square stability of the system are obtained by using the spectral analysis method. The discriminant theorem of the mobile spectrum is given by using the "non movable spectrum" as a tool. The interval stability of a linear stochastic system is studied on the basis of the interval stability of the operator spectrum definition, and the relation between the system state convergence rate and the interval (- beta, - alpha) is obtained. Linear matrix inequalities and Sc are used. The HuR complementary lemma obtains the discriminant theorem of system interval stability. On the basis of defining accurate observational and accurate energy detection, the corresponding discriminant theorems are obtained. On this basis, the system stability, accurate energy observation, accurate energy detection and the generalized Lyapunov inequality are analyzed. A numerical example is given in the section.

【學(xué)位授予單位】：山東科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O211.6

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

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2 李奇勛;;含Poisson跳線性隨機(jī)系統(tǒng)區(qū)間穩(wěn)定狀態(tài)下的系統(tǒng)狀態(tài)收斂速度分析[J];泰山學(xué)院學(xué)報(bào);2016年06期

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本文編號(hào)：1801456