發(fā)布時間：2019-05-25 02:45

【摘要】：在各種實際工程系統(tǒng)中,時滯現(xiàn)象大量存在,如信號處理、網(wǎng)絡(luò)控制系統(tǒng)、皮帶傳輸?shù)取�時滯的出現(xiàn)常常致使系統(tǒng)不穩(wěn)定和系統(tǒng)性能變差。同時,也加大了系統(tǒng)分析與綜合問題的難度。因此,分析時滯對系統(tǒng)的影響,并利用或減小這種影響一直是人們關(guān)注的熱點問題。近年來,作為時滯系統(tǒng)的重要領(lǐng)域,中立時滯系統(tǒng)因其可以同時描述系統(tǒng)狀態(tài)滯后和狀態(tài)微商滯后而受到廣泛研究。分布時滯普遍出現(xiàn)在系統(tǒng)方程中求和數(shù)量劇增且相鄰決定值之間差異變小的情況,如火箭發(fā)動機的流體火藥燃燒過程建模和材料熱加工等考慮不均勻延遲的系統(tǒng)�？陀^上看,分布時滯能夠更精確的描述系統(tǒng),揭示事物變化的本質(zhì)。因此研究分布時滯中立系統(tǒng)具有重要的實際意義。此外,考慮由于數(shù)學建模誤差、條件變化及外界干擾等引起的不確定性對系統(tǒng)的影響也是必不可少的。本文主要研究了含有分布時滯的不確定中立系統(tǒng)的魯棒濾波問題,并通過實例仿真證明了文中所提的方法是切實可行且有效的。首先,針對一類具有混合時滯的不確定中立時滯系統(tǒng),設(shè)計其魯棒H?和2L L?-濾波器�；旌蠒r滯包含離散時滯和分布時滯,并同時存在于狀態(tài)方程和輸出方程中。系統(tǒng)中的參數(shù)不確定性被假設(shè)為時變且范數(shù)有界的。通過構(gòu)造適當?shù)腖yapunov函數(shù),結(jié)合積分不等式技術(shù),建立了滿足相應(yīng)性能指標的濾波器存在的時滯依賴條件,保證濾波誤差系統(tǒng)漸近穩(wěn)定。根據(jù)所得到的規(guī)則,采用變量替換法,以線性矩陣不等式的形式給出濾波器的設(shè)計方法。仿真例子檢驗了所提方法的可行性。其次,針對具有Markov跳變參數(shù)的不確定分布時滯中立系統(tǒng),研究其魯棒H?和2L L?-濾波器的設(shè)計問題。通過建立模態(tài)依賴的Lyapunov函數(shù),利用伊藤微分和牛頓-萊布尼茲公式,提出了使濾波誤差系統(tǒng)隨機穩(wěn)定且滿足給定性能指標的濾波器存在的充分條件。利用矩陣變換等方法實現(xiàn)Lyapunov函數(shù)矩陣和系統(tǒng)矩陣之間的解耦,再經(jīng)過求解線性矩陣不等式的凸優(yōu)化問題,得到濾波器的參數(shù)。仿真算例表明設(shè)計方法的低保守性。最后,研究了非線性無窮分布時滯中立系統(tǒng)的魯棒H?和2L L?-濾波問題。系統(tǒng)中的非線性受到Lipschitz條件的約束,依據(jù)Lyapunov函數(shù)方法,引入柯西不等式處理無窮分布時滯項,充分考慮時滯相關(guān)的信息,利用積分不等式等方法,將非線性條件轉(zhuǎn)換成線性條件,給出了更易于求解的濾波器的設(shè)計方法。對于所容許的不確定性和所有能量有界的外界干擾,所設(shè)計的濾波器不僅能夠確保濾波誤差系統(tǒng)是漸近穩(wěn)定的,同時滿足相應(yīng)的擾動衰減水平。數(shù)值仿真驗證了所設(shè)計的濾波器能夠很好的還原原系統(tǒng)狀態(tài),減小了未知干擾的影響。
[Abstract]:In various practical engineering systems, there are a large number of time delay phenomena, such as signal processing, network control system, belt transmission and so on. The emergence of time delay often leads to system instability and system performance. At the same time, it also increases the difficulty of system analysis and synthesis. Therefore, it has been a hot issue to analyze the influence of time delay on the system and to make use of or reduce it. In recent years, as an important field of time-delay systems, neutral time-delay systems have been widely studied because they can describe the state delay and state derivative delay of the system at the same time. The distributed time delay generally occurs in the system equation when the summation quantity increases sharply and the difference between adjacent determining values becomes smaller, such as the modeling of fluid gunpowder combustion process of rocket engine and the thermal processing of materials. Objectively speaking, distributed time delay can describe the system more accurately and reveal the nature of the change of things. Therefore, it is of great practical significance to study the distributed delay neutral system. In addition, it is necessary to consider the uncertainty caused by mathematical modeling error, condition change and external interference. In this paper, the robust filtering problem for uncertain neutral systems with distributed delays is studied, and the simulation results show that the proposed method is feasible and effective. First of all, for a class of uncertain neutral time-delay systems with mixed delays, a robust H-H is designed for a class of uncertain neutral time-delay systems with mixed delays. And 2L / L / L filter. Mixed delays include discrete delays and distributed delays, and exist in both the equation of state and the output equation. The parameter uncertainty in the system is assumed to be time-varying and norm-bounded. By constructing the appropriate Lyapunov function and combining with the integral inequality technique, the delay dependent condition of the filter satisfying the corresponding performance index is established to ensure the asymptotic stability of the filtering error system. According to the obtained rules, the variable substitution method is used to give the design method of the filter in the form of linear matrix inequality (LMI). A simulation example is given to verify the feasibility of the proposed method. Secondly, the robust H? for uncertain distributed delay neutral systems with Markov jump parameters is studied. And the design of 2L / L / L filter. By establishing the modal dependent Lyapunov function and using Ito differential and Newton-Leibniz formula, a sufficient condition for the existence of the filter whose filtering error system is randomly stable and satisfies the given performance index is put forward. The decoupling between Lyapunov function matrix and system matrix is realized by matrix transformation, and then the convex optimization problem of linear matrix inequality is solved, and the parameters of filter are obtained. Simulation examples show the low conservatism of the design method. Finally, the robust H? And 2L / L / L filtering problem. The nonlinear in the system is constrained by the Lipschitz condition. According to the Lyapunov function method, Cauchy inequality is introduced to deal with the infinite distributed delay term, the delay related information is fully considered, and the integral inequality is used. The nonlinear condition is transformed into linear condition, and the design method of filter which is easier to solve is given. For the allowable uncertainty and all energy-bounded external interference, the designed filter can not only ensure that the filtering error system is asymptotically stable, but also satisfy the corresponding disturbance attenuation level. The numerical simulation results show that the designed filter can reduce the state of the original system and reduce the influence of unknown interference.
【學位授予單位】：東北石油大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN713

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