时滞广泛存在于很多实际控制系统之中，例如网络控制系统、电力系统等。由于时滞往往会引起系统性能恶化甚至导致系统不稳定，时滞系统的研究受到了人们的广泛关注。Lyapunov-Krasovskii泛函方法是一种研究时滞系统稳定性分析与控制问题的有效工具，但利用该方法所得结果带有一定的保守性。尽管在Lyapunov-Krasovskii泛函方法框架下涌现了大量的改进方法，但它们对时滞变化信息使用还不够充分，仍存在一定的局限性。本文在已有工作的基础上，引入切换方法，充分利用时滞变化信息，对时滞系统的稳定性分析与控制问题进行了研究。本文的具体内容如下： 针对现有时滞系统稳定性研究方法的局限性，提出了充分利用时滞变化信息的思想。把时滞区间划分为若干子区间，利用切换思想将子区间看作时滞的一个模态并将时滞变化看作不同模态之间的切换，从而把时滞系统建模为包含稳定子系统的切换时滞系统。新的系统模型等价于原系统且包含比原系统更多的可用时滞信息。在新的系统模型基础上，采用了比传统Lyapunov-Krasovskii泛函方法更为有效的模型依赖平均驻留时间方法，针对连续时间和离散时间两种情形，给出了新的指数稳定性判据并讨论了子系统个数变化对于稳定性判据的影响。 在模型依赖平均驻留时间方法的基础上，提出了一种新的切换方法并利用该方法研究了中立型时滞系统的稳定性分析与控制器设计问题。将中立型时滞系统建模为切换中立型时滞系统，然后给出了基于模型依赖平均驻留时间方法的稳定性判据。在此基础上，提出了一种新的切换方法并利用该方法给出了新的指数稳定性判据，放松了模型依赖平均驻留时间方法中对切换信号的要求。根据所得稳定性判据。提出了利用切换控制器实现系统镇定的策略并给出了该控制器的设计方案。因为充分利用时滞变化信息且不要求对整个时滞区间存在共同控制器，基于切换控制器的镇定策略保守性更小。 利用慢切换思想，围绕时滞系统的L₂增益分析与控制问题开展了研究。将时滞系统的L₂增益分析问题转化为切换时滞系统的L₂增益分析问题，利用慢切换方法给出了时滞系统稳定且具有给定L₂增益的条件。然后将所得结果推广，给出了相应的控制器设计方案。讨论了具有大时滞区间的时滞系统保成本控制问题。将具有大时滞区间的时滞系统建模为包含稳定子系统和不稳定子系统的切换时滞系统，利用慢切换方法给出了保成本控制器保证系统稳定且满足一定性能指标的充分条件。 考虑了时滞对于非线性系统的影响，解决了一类时滞神经网络系统的稳定性分析问题。将时滞神经网络系统建模为非线性切换时滞系统，从而把时滞神经网络系统的稳定性分析问题转化为切换系统的稳定性分析问题。然后利用切换方法给出了保证系统指数稳定的充分条件。 针对实际系统中可能出现的控制器失效现象，考虑了具有控制器失效的多区域时滞电力系统稳定性分析问题。为了描述控制器完全失效且经过一段时间能够恢复正常工作的现象，将多区域时滞电力系统建模为包含稳定子系统和不稳定子系统的切换多时滞系统。在新的系统模型基础上，利用慢切换方法给出了保证系统稳定的充分条件。 关键词：时滞系统；稳定性；镇定；切换方法

 Time delays are often encountered in many real control systems, such as networked control systems, power systems, etc. Since time delays may cause poor performance and even lead to instability, considerable attention has been paid to time delay systems. The Lyapunov-Krasovskii functional (LKF) approach is an efficient tool to deal with the problem of stability analysis and control for time delay systems. Although a large number of improved methods have emerged in the framework of the LKF method, the delay variation information is not adequately considered. Thus, there still exist some room for improvement. With the help of the switching method, this thesis, based on previous work of others, fully uses the delay variation information and deeply investigates the problem of stability and control for time delay systems. The main contents of this thesis are given as follows: Based on the limitations of the existing stability analysis methods for delay systems, the idea that the delay variation information should be adequately considered is proposed. The time--delay interval is divided into some smaller variable intervals. Based on the switching idea, the smaller variable interval can be viewed as a mode of the delay and the delay variation can be viewed as the switching among the modes. Then, delay systems can be modeled as switched delay systems containing stable subsystems. The new model is equivalent to the original system and contains more usable delay information. Based on the new model, the mode-dependent average dwell time (MDADT) method, which is more effective than the LKF method, is adopted to obtain stability criteria for linear continuous/discrete-time systems. The relationship between the conservativeness of the obtained results and the number of subsystems is also investigated. Based on the MDADT method, a new switching method is proposed to deal with the problem of stability analysis and stabilization for neutral delay systems. Neutral delay systems are modeled as switched neutral delay systems and then exponential stability criteria are obtained by adopting the MDADT method. Based on the obtained stability conditions, a new switching method, which can relax the constrained switching conditions in the MDADT method, is proposed and new exponential stability criteria are derived by using the method. With the help of the obtained criteria, the switching controller is used to solve the stabilization problem of neutral delay systems and new stabilization conditions are obtained. The proposed stabilization strategy is significantly less conservative due to the full use of time delay variation information and its avoidance of using a common controller for the entire delay interval. The problem of L₂ gain analysis and control for delay systems is solved by using a slow switching method. The L₂-gain analysis problem of delay systems is converted into the L₂-gain analysis problem of switched delay systems. Based on a slow switching strategy, new L₂-gain conditions are obtained and then the conditions for the existence of the L₂-gain controller are given. The problem of guaranteed cost control for uncertain systems with large delay periods (LDPs) is studied. The considered systems are modeled as switched delay systems containing a stable subsystem and an unstable subsystem. Then, sufficient conditions under which the guaranteed cost controller can keep the systems stable and guarantee an adequate level of performance are obtained by adopting a slow switching method. The effect of time delays on the stability of nonlinear system is considered and the stability analysis problem of delayed neural network systems is solved. Delayed neural network systems are modeled as nonlinear switched delay systems. The stability analysis problem of delayed neural network systems is converted into the stability analysis problem of switched systems. Then, switching methods are used and new stability conditions are derived to ensure the exponential stability of delayed neural networks. Since controller failures may occur in actual systems, the stability analysis problem of multiarea power systems with time delay under controller failures is considered. In order to describe the phenomenon that the controller is completely invalid and can restore normal work after a period of time, the considered systems are modeled as switched multi-delay systems containing a stable subsystem and an unstable subsystem. Based on the new model, sufficient stability conditions which can guarantee the stability of the considered systems are obtained by using a slow switching method. Key Words: Time delay systems; stability; stabilization; switching technique