【作者】 夏君华；

【导师】 王向东；

【作者基本信息】 沈阳工业大学 ， 控制理论与控制工程， 2003， 硕士

【摘要】 混杂动态系统是指系统既包含连续动态变量又包含离散动态变量，而且两种变量相互作用形成系统。其中连续变量往往对应于实际系统中的连续动态，而离散变量则多种多样，既可能是数据采样，也可能是逻辑切换、系统结构的变化、平衡点的转移等等。这种新的系统与以往的所研究的单纯的连续系统或离散系统有所不同，系统的描述相对复杂，也更能精确合理地刻画现实世界中的各种问题。 切换系统是混杂动态系统的一类重要类型。一般地说，切换系统由若干个子系统以及一个切换法则构成，并通过在子系统之间的进行切换实现预定的性能指标。切换系统在很多实际工程应用中经常遇到，如飞机的多工作点切换控制，电力系统网络的切换以及多频采样数字系统的控制等。切换系统的本质是切换，其性质不是各个子系统性质的简单迭加，而是具有其特殊性和复杂性。因此，切换系统稳定性的研究是非常必要的，在理论和实践上都有重要的意义。本论文主要研究了切换系统的指数稳定性问题，并给出了保证系统切换指数稳定的充分条件。 本文的内容的安排如下： 第一章介绍了混杂动态系统及切换系统的发展历史和实际背景，前人对切换系统的研究进展及研究方法，最后概述了本文的主要工作。 第二章引入了切换系统数学模型。首先，我们分别给出了外部促使切换和内部促使切换单独的数学模型，并给出几个实际例子对模型进行说明；其次，将它们组合在一起，建立切换系统的一般模型，最后将该切换系统模型与混杂动态系统模型比较，说明它的适用性。 第三章利用多Lyapunov函数方法，研究了非线性切换系统的指数稳定性。首先介绍了多Lyapunov函数方法以及前人应用该方法取得的一些结果，并对这些结果进行比较说明；其次，我们应用多Lyapunov函数方法研究了一类切换系统的指数稳定性，得到了系统指数稳定的充分条件，并将结果推广到带有不确定性的切换系统中，然后将定理验证转化为LMIs问题，使得定理充分条件成为较易检验的代数条件，最后用仿真和数值例子说明了结果的正确有效性。沈阳工业大学硕士学位论文 第四章利用向量投影理论研究线性切换系统的稳定性以及构造一种切换法则。首先介绍向量投影理论以及前人得到的稳定性结果;其次，利用向量投影理论给出线性切换系统指数稳定充分条件，在一定条件下，可以推广到一类带有持续扰动系统中并得到其稳定的充分条件，同时基于稳定性条件设计了一种切换法则，然后用仿真和数值例子说明了结果的正确有效性。 本文的最后是总结与展望。更多还原

【Abstract】 Hybrid dynamic systems are those where the behavior of interest is determined by interacting continuous and discrete dynamics. Continuous dynamics may be considered as the continuous variables while the discrete ones may be considered as versatile incidents, such as sampled-data, logic switching, transformation of system structure and shift of balance point, et, al. The systems are different from single continuous systems or discrete ones in that their systems description is comparatively complicate and more precisely and reasonably depict the problem in the real world.Switched systems are one of the important classes of hybrid dynamic systems, which consist of a family of continuous-time subsystems and a rule that orchestrates the switching between them to achieve the expected performance. Switched systems are widely used in many practical problems, such as switching control of multiple work modes of planes, web switching of electric systems and sampled-data control systems, et, al. The nature of switched systems is switching, however it is not the simple addition of those of different subsystems and has some particularity and complexity. Therefore, the investigation of switched systems is very necessary and has important significance in theory and practice. This dissertation mainly discusses the exponential stability of switched systems and the sufficient conditions of exponential stability are presented.This dissertation is organized as follows:In Chapter 1, we briefly review the history and background of hybrid dynamic systems and switched systems. The methods and techniques used in studying switched systems are introduced and the recent development of switched systems is also presented in this part.The constitution of mathematie model of switched systems is studied in Chapter 2. Firstly, the models of externally forced switching and internally forced switching are founded respectively and two examples are given to explain them. Then, we combine them together to get a uniform model of switched systems and compare with the model of hybrid dynamic systems to show it applicability.In Chapter 3, the exponential stability of switched nonlinear systems is studied. In first, we introduce the method of multiple Lyapunov functions and preceding theory results, and compare with them. In second, using this method, we discuss the exponential stability of switched nonlinear systems and give the sufficient conditions of stability; Furthermore, exponential stability of a class of switched systems with uncertainty is investigated. Mean while, we may translate theorem test into the LMIs problem. In the end, simulation examples are given to show the validity of the result.In Chapter 4, using the vector projection theory, the exponential stability of switched systems is investigated. Firstly, we introduce the vector projection theory and preceding theory results. Secondly, the sufficient conditions of stability linear switched systems are presented; Furthermore, the sufficient conditions of stability of nonlinear switched systems are extended under some conditions. Meanwhile, we design a kind of switching law based on the conditions. Finally, simulation examples are given to show the validity of the result.In the end, there are summary and prospect.更多还原