切换线性系统的若干动力学性质研究

项目名称： 切换线性系统的若干动力学性质研究

项目编号： No.61273007

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 刘兴文

作者单位： 西南民族大学

项目金额： 61万元

中文摘要： 切换系统是混杂系统的一个主要分支, 可以建模大量的实际系统。由于具有多个子系统和灵活的切换方式，其动力学性质非常丰富。切换系统有两个重要特征：其动力学性质远比一般动力学系统复杂；切换信号对切换系统的动力学有着至关重要的影响。本项目从切换系统的基本特征出发，重点研究四个问题：一、揭示切换正系统和切换定号系统的动力学性质，并研究它们在一般切换系统中的应用方法。二、揭示互为对偶的切换系统间动力学性质的关系以及切换系统不同动力学性质间的关系，创新切换系统的研究方法。三、建立时滞切换系统在给定切换信号集上的动力学性质(指数稳定性, 渐近稳定性和收敛性)一致性的判定条件。四、建立切换系统各种Pseudo-稳定性的判定条件。本项目力图从新的角度展开研究，提出研究切换系统的新思路，联系该领域的研究前沿，从事具有挑战性的工作，具有重要的理论意义。因为切换系统有深刻的实际背景，本项目的结果具有广阔的应用前景。

中文关键词： 时滞；切换系统；对偶系统；稳定性；非线性系统

英文摘要： Switched systems are one of the main branches of hybrid systems, which can be used to model many practical systems. Since switched systems have multiple subsystems and flexible switching patterns, they exhibit abundant dynamic characteristics. In general, switched systems have two main features: one is that their dynamics is much more complex than that of general dynamic systems, and another one is that switching signals have important impact on the dynamics of systems. Based on these two basic features, this proposal will address the following four aspects: (1) The dynamics of switched positive systems and switched definite systems will be studied, and the findings will be applied to study the dynamics of general switched systems. (2) The relationship between the dynamics of two mutually dual switched systems and the relationship between different dynamics (mainly including exponential stability, asymptotic stability, and attractivity) of a switched system will be explored. This will lead to a new approach to investigate the dynamics of switched systems. (3) For given sets of switching signals, the conditions that are able to judge whether the dynamics (including exponential stability, asymptotic stability, and convergence) of a switched system with time-delay is uniform or not will be derived. (4) The criter

英文关键词： Delay；switched systems；dual systems；stability；nonlinear systems