【摘要】：正系統(tǒng)是一類在現(xiàn)實(shí)中很常見的系統(tǒng),比如:人口模型、經(jīng)濟(jì)發(fā)展模式等等。它是一類當(dāng)初始條件和輸入為非負(fù)值時(shí),系統(tǒng)的狀態(tài)和輸出始終為非負(fù)值的動(dòng)態(tài)系統(tǒng)。切換系統(tǒng)作為一種不可或缺的混合系統(tǒng),在機(jī)房管理、交通系統(tǒng)、電力系統(tǒng)等有很好的應(yīng)用。它是由子系統(tǒng)和切換規(guī)則組成。切換正系統(tǒng)是由有限個(gè)正子系統(tǒng)和切換信號(hào)組成的一類系統(tǒng)。在過去十年里,切換正系統(tǒng)在通信、醫(yī)療、自動(dòng)化等范圍內(nèi)吸引了愈來愈多研究者的注意力。按照切換正系統(tǒng)在不同應(yīng)用中發(fā)揮的作用來看,它要符合兩點(diǎn)性質(zhì),正的且具有切換律。應(yīng)當(dāng)指出:切換正系統(tǒng)在很多問題的研究上與上述兩種系統(tǒng)相比具有很大的挑戰(zhàn)性。論文從以下幾個(gè)方面展開研究:第一章是緒論。論述了切換正系統(tǒng)的研究意義,總結(jié)了切換正系統(tǒng)研究的一些主要問題及現(xiàn)狀。結(jié)合切換正系統(tǒng)的一些理論問題,如:穩(wěn)定、鎮(zhèn)定、觀測(cè)等。根據(jù)這些問題介紹了解決切換正系統(tǒng)問題所需要的方法和工具。最后,介紹了本文的主要內(nèi)容和框架。第二章探討了多胞體切換正系統(tǒng)的魯棒鎮(zhèn)定問題。首先,利用多線性余正Lyapunov函數(shù)方法,探討了多胞體切換正系統(tǒng)的鎮(zhèn)定問題。其次,借助線性規(guī)劃方法,給出多胞體切換正系統(tǒng)全局指數(shù)穩(wěn)定的充分條件,設(shè)計(jì)出狀態(tài)反饋控制律,解決了多胞體切換正系統(tǒng)的鎮(zhèn)定問題。本章最后給出的仿真案例聲明了提出方法的有效性。第三章研究了改進(jìn)的切換正系統(tǒng)的鎮(zhèn)定問題。利用矩陣分解方法,設(shè)計(jì)出新的控制器,構(gòu)造出新的系統(tǒng)反饋控制律,使增益矩陣的秩不再局限為1,降低了結(jié)論的保守性。同時(shí),使得給出的系統(tǒng)既是正的又是穩(wěn)定的。最后,通過仿真驗(yàn)證了提出方法的有效性。第四章考慮了切換正系統(tǒng)具有l(wèi)_1增益的鎮(zhèn)定設(shè)計(jì)。利用多線性余正Lyapunov函數(shù),建立了使系統(tǒng)基于平均駐留時(shí)間上鎮(zhèn)定的充分條件。同時(shí),給出了使系統(tǒng)鎮(zhèn)定的反饋控制律,得到了L_1增益。最后,舉例檢驗(yàn)給出方法的可行性。第五章是總結(jié)與展望。首先,總結(jié)了本文的重要結(jié)論。其次,提出了今后可能進(jìn)行研究的問題。
[Abstract]:Positive system is a kind of system that is very common in reality, such as population model, economic development model and so on. It is a kind of dynamic system whose state and output are always non-negative when the initial condition and input are non-negative. As an indispensable hybrid system, switching system has a good application in computer room management, traffic system, power system and so on. It consists of subsystems and switching rules. Switched positive system is a class of systems composed of finite positive subsystems and switched signals. In the past decade, switching forward systems have attracted more and more researchers' attention in the fields of communication, medicine, automation and so on. According to the function of switched positive system in different applications, it should conform to two-point property, positive and have switching law. It should be pointed out that switched forward systems are more challenging than these two systems in many problems. The thesis starts the research from the following aspects: the first chapter is the introduction. This paper discusses the significance of the research of switched forward system, and summarizes some main problems and present situation of the research of switched forward system. Combined with some theoretical problems of switched positive systems, such as stability, stabilization, observation and so on. According to these problems, the methods and tools needed to solve the problem of switching forward system are introduced. Finally, the main contents and framework of this paper are introduced. In chapter 2, the problem of robust stabilization for multibody switched positive systems is discussed. Firstly, the stabilization problem of multi-cell body switching positive systems is discussed by using the method of multi-linear copositive Lyapunov function. Secondly, by means of linear programming, sufficient conditions for the global exponential stability of the positive system with multiple cell bodies switching are given, and the state feedback control law is designed to solve the stabilization problem of the positive system with multiple cell body switching. At the end of this chapter, a simulation case is given to illustrate the effectiveness of the proposed method. In chapter 3, we study the stabilization of improved switched forward systems. By using matrix decomposition method, a new controller is designed and a new feedback control law is constructed. The rank of the gain matrix is no longer limited to 1, which reduces the conservatism of the conclusion. At the same time, the given system is both positive and stable. Finally, the effectiveness of the proposed method is verified by simulation. In chapter 4, we consider the stabilization design of switched positive systems with L _ S _ 1 gain. By using the multilinear copositive Lyapunov function, a sufficient condition is established to stabilize the system based on the average dwell time. At the same time, the feedback control law of stabilizing the system is given, and the L _ S _ 1 gain is obtained. Finally, the feasibility of the method is verified by examples. The fifth chapter is the summary and prospect. Firstly, the important conclusions of this paper are summarized. Secondly, the possible problems in the future are put forward.
【學(xué)位授予單位】：杭州電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP13

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