本文選題：時(shí)滯 + 隨機(jī)微分系統(tǒng)��； 參考：《四川師范大學(xué)》2017年碩士論文

【摘要】：隨機(jī)時(shí)滯微分系統(tǒng)是一種重要的數(shù)學(xué)模型,穩(wěn)定性是隨機(jī)時(shí)滯微分系統(tǒng)的一個基本問題.時(shí)滯和隨機(jī)干擾常常會導(dǎo)致系統(tǒng)的穩(wěn)定性變化.建立隨機(jī)時(shí)滯微分系統(tǒng)穩(wěn)定性的判別條件非常重要.通過構(gòu)造恰當(dāng)?shù)腖yapunov泛函(或函數(shù))來研究系統(tǒng)的穩(wěn)定性是通常的做法,但構(gòu)造Lyapunov泛函有一定的難度.使用其他技巧來研究隨機(jī)時(shí)滯微分系統(tǒng)的穩(wěn)定性是一種選擇.本文中,我們將采用不等式技巧來研究隨機(jī)時(shí)滯微分系統(tǒng)的穩(wěn)定性,以避免Lyapunov泛函構(gòu)造的困難.首先,對系統(tǒng)建立了一個適當(dāng)?shù)某?shù)變易公式,并利用Jesen不等式、Burkholder-Davids-Gundy不等式、Holder不等式等分析技巧,得到了系統(tǒng)的吸引性和p-階矩穩(wěn)定性的充分條件,并給出數(shù)值實(shí)例,驗(yàn)證本文結(jié)果的有效性.其次,給出了隨機(jī)時(shí)滯微分系統(tǒng)K-穩(wěn)定性概念,并通過非負(fù)矩陣性質(zhì)、BDG不等式、Holder不等式、反證等分析技巧建立了系統(tǒng)的K-全局p階矩漸近穩(wěn)定和K-全局p階矩指數(shù)穩(wěn)定.
[Abstract]:Stochastic delay differential system is an important mathematical model and stability is a basic problem of stochastic delay differential system. Time delay and random disturbance often lead to the stability change of the system. It is very important to establish the stability criteria for stochastic delay differential systems. It is common to study the stability of the system by constructing proper Lyapunov functional (or function), but it is difficult to construct Lyapunov functional. It is an option to use other techniques to study the stability of stochastic delay differential systems. In this paper, we will use inequality techniques to study the stability of stochastic delay differential systems so as to avoid the difficulty of constructing Lyapunov Functionals. First of all, an appropriate constant variation formula is established for the system. By using the analytical techniques such as the Jesen inequality and Burkholder-David Gundy inequality and Holder inequality, the sufficient conditions for the attractiveness of the system and the stability of the p-order moment are obtained, and a numerical example is given. The validity of the results is verified. Secondly, the concept of K-stability for stochastic delay differential systems is given, and the asymptotic stability of K-global p-order moments and the exponential stability of K-global p-order moments are established by using the nonnegative matrix properties of BDG inequality Holder inequality, inverse proof and other analytical techniques.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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