本文選題：指數(shù)穩(wěn)定　切入點(diǎn)：有限時間穩(wěn)定　出處：《陜西師范大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：本文主要研究離散切換正系統(tǒng)的穩(wěn)定性與鎮(zhèn)定性.首先,本文研究了離散切換正系統(tǒng)的指數(shù)穩(wěn)定和鎮(zhèn)定問題.其次,當(dāng)控制器的切換時刻滯后于對應(yīng)子系統(tǒng)的切換時刻時,本文進(jìn)一步研究了離散切換正系統(tǒng)的異步鎮(zhèn)定和異步有限時間控制.最后,本文也進(jìn)一步討論了離散正奇異時滯系統(tǒng)的指數(shù)穩(wěn)定和離散切換正奇異系統(tǒng)的有限時間穩(wěn)定等問題.主要內(nèi)容如下:第一章介紹了切換系統(tǒng),切換正系統(tǒng),Lyapunov穩(wěn)定及有限時間穩(wěn)定的基本知識.為了給出離散正奇異系統(tǒng)的解,進(jìn)一步介紹了廣義逆的相關(guān)理論.第二章研究了離散切換正系統(tǒng)的穩(wěn)定性和鎮(zhèn)定性問題.首先,通過構(gòu)造多線性協(xié)正Lyapunov函數(shù),利用前向模型依賴平均駐留時間切換信號,得到了離散切換正系統(tǒng)指數(shù)穩(wěn)定的一個充分條件.并指出,當(dāng)切換信號滿足一定的假設(shè)條件時,前面文獻(xiàn)中的一些結(jié)果可以看作是該結(jié)果的一個推論.其次,基于多采樣類-Lyapunov函數(shù)差分的方法,得到了線性離散切換正系統(tǒng)指數(shù)穩(wěn)定的另一個充分條件.根據(jù)所得結(jié)論,設(shè)計(jì)了一類模型依賴狀態(tài)反饋控制器使得閉環(huán)系統(tǒng)在前向模型依賴平均駐留時間切換信號下是正的且是指數(shù)穩(wěn)定的.最后,給出了兩個數(shù)值例子說明了所得理論結(jié)果的正確性.第三章討論了含有時變時滯的離散切換正系統(tǒng)的異步鎮(zhèn)定性.首先,通過構(gòu)造適當(dāng)?shù)腖yapunov-Krasovskii泛函,得到了離散切換正時滯系統(tǒng)在模型依賴平均駐留時間切換信號下指數(shù)穩(wěn)定的一個充分條件.其次,通過允許所選擇的Lyapunov-Krasovskii泛函在被激活的子系統(tǒng)和控制器不匹配的時間區(qū)間內(nèi)遞增,基于模型依賴平均駐留時間切換信號,得到了存在一類狀態(tài)反饋控制器使得閉環(huán)系統(tǒng)在異步切換下是正的且是指數(shù)穩(wěn)定的充分條件.最后,給出兩個數(shù)值例子說明了所提出方法的有效性.第四章討論了離散脈沖切換正時滯系統(tǒng)在異步切換下的有限時間控制.首先,通過構(gòu)造一個適當(dāng)?shù)腖yapunov函數(shù),得到了離散脈沖切換正時滯系統(tǒng)在模型依賴平均駐留時間切換信號下有限時間穩(wěn)定的一個充分條件.其次,通過構(gòu)造另一個不同的Lyapunov函數(shù),得到了存在一類狀態(tài)反饋控制器使得閉環(huán)系統(tǒng)在異步切換下是正的且是有限時間穩(wěn)定的幾個充分條件,并給出了控制器增益的具體形式.最后,給了一個數(shù)值例子說明了所得結(jié)果的有效性和可行性.第五章研究了離散正奇異時滯系統(tǒng)的指數(shù)穩(wěn)定性.首先,利用奇異值分解和單模坐標(biāo)變換,得到了離散奇異時滯系統(tǒng)是正的一個充要條件.其次,通過構(gòu)造適當(dāng)?shù)木�性協(xié)正Lyapunov函數(shù),得到了離散正奇異時滯系統(tǒng)指數(shù)穩(wěn)定的一個充分條件.并且,所得到的結(jié)果都是以代數(shù)矩陣不等式的形式給出的,它們可以利用Matlab中的線性規(guī)劃工具箱數(shù)值的進(jìn)行求解.最后,給出了一個數(shù)值例子說明了所提出方法的有效性.第六章討論了離散切換正奇異系統(tǒng)的有限時間穩(wěn)定問題.首先,提出了離散切換正奇異系統(tǒng)有限時間穩(wěn)定的概念,并給出了一個假設(shè)條件保證離散切換正奇異系統(tǒng)具有相容切換.其次,利用狀態(tài)轉(zhuǎn)移矩陣,得到了當(dāng)離散切換正奇異系統(tǒng)具有相容切換時,其在任意切換下有限時間穩(wěn)定的充要條件.進(jìn)一步,通過構(gòu)造擬線性Lyapunov函數(shù),基于模型依賴平均駐留時間切換信號,以代數(shù)矩陣不等式的形式給出了離散切換正奇異系統(tǒng)在相容切換下有限時間穩(wěn)定的另一個充分條件.最后,給出了 一個數(shù)值例子表明了所提出方法的有效性.
[Abstract]:This paper mainly studies the stability and the town of discrete-time switched positive systems qualitatively. Firstly, in this paper the discrete switched positive systems exponential stability and stabilization problem. Secondly, when the time of the switching controller switching time lag in the corresponding subsystem, this paper further studies the discrete switching stabilization system is asynchronous and asynchronous finite time control. Finally, this paper also further discusses the discrete singular time-delay systems and exponential stability of discrete switched singular systems are finite time stability problems. The main contents are as follows: the first chapter introduces the switching system, switching system, the basic knowledge of Lyapunov stability and finite time stability of discrete singular system is given. In order to further introduce solutions. The theory of generalized inverse. The second chapter studies the stability and stabilization of discrete-time switched positive systems. Firstly, by constructing multiple linear copositive Lyapu The Nov function, the forward model depends on average dwell time switching signal, a sufficient condition is obtained for the exponential stability of discrete-time switched positive systems. And pointed out that when the switching signal satisfies certain assumptions, some in front of the results in the literature can be seen as a corollary of this result. Secondly, multi class -Lyapunov function difference based method, another sufficient condition is obtained for linear discrete-time switched system is exponentially stable. According to the conclusion, design a kind of model dependent state feedback controller such that the closed-loop system in the forward model depend on average dwell time switching signal is positive and is exponentially stable. Finally, two numerical example is given to illustrate the correctness of the theoretical results. The third chapter discusses the asynchronous stabilization of discrete-time switched positive systems with time-varying delay. Firstly, by constructing appropriate Lyapunov-Kraso The vskii function, obtained discrete switched systems with time delay is dependent on a sufficient condition of average dwell time switching exponential stability in the model. Secondly, by allowing the choice of Lyapunov-Krasovskii functional mismatch in the sub system and the controller is activated by the time interval increases, the model depends on average dwell time switching signals are obtained based on the a state feedback controller such that the closed-loop system under asynchronous switching is positive and the sufficient conditions of exponential stability. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method. The fourth chapter discusses the discrete pulse finite time under asynchronous switching control is switched delay systems. Firstly, by constructing a the appropriate Lyapunov function, the Discrete Impulsive Switched Systems with time delay is dependent on the average dwell time switching signal in a finite time stability model A sufficient condition. Secondly, by constructing a different Lyapunov function, the existence of a state feedback controller such that the closed-loop system under asynchronous switching is positive and some sufficient conditions for finite time stability, and gives the specific form of controller gain. The most effective, gave a numerical example to illustrate the obtained results and feasibility. The fifth chapter studies the exponential stability of discrete singular time-delay systems. Firstly, by using singular value decomposition and single mode coordinate transformation, the discrete singular time-delay systems is a necessary and sufficient condition is. Secondly, through linear co constructing Lyapunov function, a sufficient condition is given index of discrete singular time-delay systems is stable. And the results are given in the form of algebraic matrix inequality, they can use the linear programming tool box in Matlab number The values are solved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. The sixth chapter discusses the finite time discrete switched singular systems are stable. First, put forward the concept of discrete switching is singular finite time stability of the system, and gives an assumption to guarantee the discrete-time switched positive singular the system has compatibility switch. Secondly, using the state transition matrix is obtained when the discrete singular systems with switching are compatible when switching, the necessary and sufficient conditions for finite time stability under arbitrary switching. Further, by constructing a quasi linear Lyapunov function model depends on average dwell time switching signal based on the given by the discrete algebraic matrix inequalities switching is singular system in another sufficient condition of finite time stability compatible switching. Finally, a numerical example is given to show that the proposed method Effectiveness.

【學(xué)位授予單位】：陜西師范大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O231

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本文編號：1618156