时滞切换系统的若干关键动力学性质研究

切换系统是混杂系统的重要分支，可建模大量的实际复杂系统。因时滞广泛存在并对系统产生重要的影响，时滞切换系统展示出复杂的动力学行为。向量场不连续且具有无穷维的基本特征决定了该领域还存在大量未知性质。本项目主要研究三个关键动力学性质。1、建立不同稳定性之间的等价关系，将强稳定性转化为对弱稳定性的研究。2、研究指数型输入-状态稳定性，揭示它与标称系统指数稳定性之间的内在联系。3、研究时滞切换非线性系统的线性化问题，铺平线性系统理论应用于非线性系统的道路。由于实际系统都是非线性的，该项研究为实际系统的分析和设计奠定了理论基础。本项目力图从新的角度为时滞切换系统的分析与综合提供有效新工具和方法，为进一步研究混杂系统提供思想和技术上的启迪，具有很大的挑战性和重要的理论意义。由于时滞切换系统有着深刻的实际背景，项目成果具有广阔的应用前景。

As one of the most important branches of hybrid systems, switched systems are capable of modelling vast complex engineering systems in real life. Since delays widely exist in almost all systems and have various impacts on their dynamics, delayed switched systems exhibit complicated dynamical behaviors. Characterized by discontinuity of vector fields and infinite dimensional state space, switched systems display many properties requiring further exploration. On this ground, this proposal is mainly concerned with the following three important dynamical properties. 1. Establish an equivalent relationship between different stabilities and derive strong stability conclusion from relatively weak conditions. 2. Investigate the property of exponential-type input-state stability and reveal the inherent relationship between the property and the exponential stability of nominal system. 3. Research the linearization issue of switched nonlinear systems with delays, paving the way of applying linear system theory to nonlinear systems. Since all the practical systems are actually nonlinear, this study lays theoretical bases for analyzing and designing such systems. In a word, this project seeks to provide effective new tools and methods for the analysis and synthesis of delayed switching systems and therefore is challenging and of theoretical significance. The proposal also provides ideological and technical inspiration for further research on hybrid systems. Due to the profound practical backgrounds of delayed switched systems, the findings of the project have broad potential applications in the future.