摘要
时滞现象在实际系统中是普遍存在的，且往往是导致系统性能恶化的主要原因之一。由于时滞相关的稳定性及控制结果提供了使得系统保持稳定的时滞的大小，因而比时滞无关的稳定性结果具有较少的保守性，近年来吸引了许多研究者的关注和重视。故而时滞及时变时滞系统时滞相关的鲁棒稳定性和控制的研究有着重要的意义。
本文的课题来源于国家自然科学基金重点项目(重点项目编号：60334010，面上项目编号：60474047)，高等学校博士学科点专项基金(项目编号：20030561013)及广东省自然科学基金(项目编号：31406)。利用Lyapunov-Krasovskii泛函，矩阵不等式技巧和非线性处理方法等，结合LMI技术，本文比较系统的研究了时滞系统及时变时滞系统以及在有非线性扰动情况下的时滞相关鲁棒稳定性和控制，H_∞鲁棒控制，输出反馈H_∞鲁棒控制，离散时间时滞系统的H_∞控制，Lurie时变时滞不确定控制系统的时滞相关绝对稳定性，以及时滞系统应用在网络化控制系统的鲁棒镇定等的问题。主要研究工作的内容包括：
1．通过谱半径和模矩阵相关理论，针对线性不确定多时滞系统，在只要求系统矩阵为Hurwitz矩阵的条件下，建立了一个新的且更少保守性的稳定性判据的结果。
2．研究了带非线性扰动的多常时滞系统和时变时滞不确定系统的时滞相关鲁棒稳定性。基于Lyapunov-Krasovskii泛函，根据矩阵不等式技术和非线性处理方法，给出了非线性扰动的多常时滞系统和多时变时滞不确定系统的时滞相关H_∞鲁棒稳定性的新结果。得到结果与已有文献的结果相比具有更少保守性。
3．研究了不确定多时不变时滞Lurie直接控制系统的绝对稳定性，以及不确定多时变时滞Lurie直接和间接控制系统的绝对稳定性，得到了一些新的时滞相关绝对稳定性的充分条件。该结果与已有文献的结果相比具有更少保守性。
4．结合二次型性能指标研究了一类带非线性扰动的不确定多时变时滞系统的保性能H_∞鲁棒控制问题，给出了一个新的无记忆状态反馈保性能控制器的充分条件。
5．首先研究了带非线性扰动的不确定多时变时滞系统的输出反馈H_∞鲁棒控制，得到了新的输出反馈镇定判据。其次在频域法中研究线性多定常时滞
Time delay, widely existing in the practical systems, often is one of the main reason of causing the system performance deterioration and even instable. Delay-dependant results have less conservative than the delay-independent ones, for the results of delay-dependent stability and control provide the size of delays such that the systems keeps stable. Therefore, many researchers pay much attention and make some efforts on it. So the study of delay-dependent stability and control for the time-invariant delay systems and time-varying delay systems is significant.
The research mainly comes from the supports of National Nature Science Foundation of China (Key Project No. 60334010, Project No. 60474047); SRFDP (Project No. 20030561013), and Guangdong Province Natural Science Foundation of China (Project No. 31406). In terms of Lyapunov-Krasovskii functional, matrix inequality tactics, and the method for dealing with nonlinear term, delay-dependent stability and control of the time invariant delay systems and time-varying delay systems, even with nonlinear perturbations, are systematically studied, such as H∞ robust stability, output feedback H∞ robust control, Hoo robust control for discrete time delay systems, absolute stability for Lurie uncertain time-delay systems and robust stabilization of networked control systems. Main studies include as follows:
1. A new stability criterion of linear uncertain systems with multiple delays is obtained based on the related theory of spectral radius and modulus matrix by the frequency domain method. The results are presented based on the assumption that system matrix A is a Hurwitz one and there is no requirement of a negative matrix measure.
2. Delay-dependent stability of uncertain time-varying or time-invariant delay systems with nonlinear perturbation is studied. Based on Lyapunov-Krasovskii functional and matrix inequality methods, sufficient conditions of delay-dependent H∞ robust stability are presented.
3. Absolute stability of uncertain multiple time-varying or time-invariant delay Lurie direct control systems and uncertain multiple time-varying delay Lurie indirect control systems are studied. In terms of matrix inequality technique and the method for dealing with nonlinear term, new sufficient conditions of delay-dependent absolute stability are provided, which by some examples are
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