本文選題：Lurie系統(tǒng) + T-S模型��； 參考：《杭州電子科技大學(xué)》2015年碩士論文

【摘要】：Lurie時(shí)滯系統(tǒng)是非線性控制中不可缺少的組成部分，這類系統(tǒng)的概念由Lurie在1944年研究一個(gè)非線性控制模型系統(tǒng)時(shí)提出來(lái)。這個(gè)系統(tǒng)可以簡(jiǎn)化成線性部分和非線性部分，線性部分用準(zhǔn)確的模型描述，且要求穩(wěn)定，非線性部分要求其為連續(xù)并且包含在由兩條直線組成的扇形區(qū)域內(nèi)。本文主要研究?jī)深怢urie時(shí)滯系統(tǒng)的絕對(duì)穩(wěn)定性分析和濾波器的設(shè)計(jì)。研究?jī)?nèi)容主要包括三個(gè)部分： 第一部分：考慮一類中立型Lurie時(shí)滯系統(tǒng)，這類系統(tǒng)帶有常數(shù)混合時(shí)滯，研究其絕對(duì)穩(wěn)定性問(wèn)題。首先，利用時(shí)滯分解方法，將狀態(tài)時(shí)滯分割為小區(qū)間，構(gòu)造新型Lyapunov-Krasovskii泛函，分別在無(wú)限扇形區(qū)間的條件和有限扇形區(qū)間條件下，，運(yùn)用矩陣不等式處理技巧得到系統(tǒng)絕對(duì)穩(wěn)定的充分條件。接著，進(jìn)一步深入考慮系統(tǒng)在帶有不確定條件下，這類系統(tǒng)在有限扇形條件下的絕對(duì)穩(wěn)定性條件。 第二部分：在狀態(tài)時(shí)滯是時(shí)變情況下，考慮一類帶有中立型Lurie時(shí)變系統(tǒng)的絕對(duì)穩(wěn)定性問(wèn)題。其中中立時(shí)滯是常數(shù)時(shí)滯且狀態(tài)時(shí)滯是變時(shí)滯，時(shí)變時(shí)滯在一定區(qū)間內(nèi)，通過(guò)對(duì)時(shí)變時(shí)滯劃分成小區(qū)間，使得每個(gè)區(qū)間片段構(gòu)成新的Lyapunov-Krasovskii泛函，并通過(guò)Leibniz-Newton公式引入自由權(quán)矩陣，在無(wú)限扇形區(qū)間的條件下，最后得到線性矩陣不等式形式的絕對(duì)穩(wěn)定條件。 第三部分：對(duì)一類基于T-S模型的Lurie型時(shí)變時(shí)滯系統(tǒng)，在有限扇形條件下，研究其∞濾波問(wèn)題。這個(gè)部分主要根據(jù)線性矩陣不等式技術(shù)得到時(shí)滯相關(guān)的設(shè)計(jì)結(jié)果，通過(guò)尋求一個(gè)依賴于時(shí)滯變化的Lyapunov-Krasovskii泛函，引入自由權(quán)矩陣的方法，對(duì)得到的濾波誤差系統(tǒng)進(jìn)行穩(wěn)定性分析，由于在矩陣不等式中出現(xiàn)了耦合的矩陣變量，再利用所得結(jié)果結(jié)合矩陣解耦合的方法，使其保守性進(jìn)一步降低。 每一部分內(nèi)容最后，都給出相應(yīng)的數(shù)例驗(yàn)證結(jié)果。
[Abstract]:Lurie time-delay system is an indispensable part of nonlinear control. The concept of this kind of system was proposed by Lurie when he studied a nonlinear control model system in 1944. The system can be simplified into linear part and nonlinear part. The linear part is described by an accurate model and it needs to be stable. The nonlinear part needs to be continuous and contained in a sector region composed of two straight lines. In this paper, the absolute stability analysis and filter design of two classes of Lurie time-delay systems are studied. In the first part, we consider a class of neutral Lurie time-delay systems with constant mixed delays and study its absolute stability. First of all, by using the time-delay decomposition method, the state delay is divided into small intervals, and a new Lyapunov-Krasovskii functional is constructed, under the conditions of infinite sector interval and finite sector interval, respectively. The sufficient conditions for the absolute stability of the system are obtained by using matrix inequality processing techniques. Then, the absolute stability conditions of this kind of systems under the condition of finite sector shape are further considered under the condition of uncertainty. In the second part, we consider the absolute stability of a class of Lurie time-varying systems with neutral type when the state delay is time-varying. The vertical delay is a constant delay and the state delay is a variable delay. The time-varying delay is in a certain interval. By dividing the time-varying delay into small intervals, each segment of the interval forms a new Lyapunov-Krasovskii functional, and the free right matrix is introduced by Leibniz-Newton formula. Under the condition of infinite sector interval, the absolute stability condition in the form of linear matrix inequality is obtained. Part three: for a class of Lurie time-varying time-delay systems based on T-S model, the 鈭

本文編號(hào)：2016940