【作者】 王汝凉；

【导师】 刘永清；

【作者基本信息】 华南理工大学 ， 控制理论与控制工程， 2001， 博士

【摘要】 由于计算机技术的迅猛发展，近来，离散系统的研究再次引起工程、控制和科学界的特别重视。本文研究离散时滞广义系统的鲁棒稳定性与控制，主要内容包括以下几个部分： (Ⅰ) 离散(时滞)广义系统模型的一般解、局部能达性与局部能控性 首次利用Z-变换得到了带时滞与不带时滞离散广义系统解的新的表达式，并且获得了系统局部能达与局部能控性的充分必要条件。同时，给出了数值例子。 (Ⅱ) 离散时滞与二次时滞广义系统的稳定域的定性、定量分析 首先利用Lyapunov方法定性、定量讨论了离散时滞与二次时滞广义系统并给出了零解一致稳定区域和渐近稳定区域的定量估计。接着，对于适当小的滞后，建立了该类系统的零解一致稳定和一致渐近稳定的代数判据；该判据既是定性也是定量的。最后提出了怎样求最大稳定区域的一个重要的问题。 (Ⅲ) 多时滞离散广义系统的稳定性和鲁棒稳定性 首先对多时滞离散广义系统，给出了两个渐近稳定性判据。其中之一可直接检验，另一个通过边界检验。其次我们获得了多时滞不确定离散广义系统独立于时滞的容易计算的鲁棒稳定性判据，并且提供了稳定和性能鲁棒性的有效度量方法。 (Ⅳ) 多时滞离散不确定广义系统极点配置的鲁棒性 给出了多时滞离散不确定广义系统的所有有限极点位于一个特殊区域内的充分性判据。该区域的形状没有附加特别限制，当所有极点按要求限制在稳定区域内时，所给出的判据将成为鲁棒稳定性判据。 (Ⅴ) 带扰动离散时滞广义系统的鲁棒D-稳定性分析 从不同的扰动参数类型研究了带扰动离散时滞广义系统，给出了鲁棒D-稳定性判据，这些判据能保证带扰动离散时滞广义系统的所有广义特征值位于一个特殊的圆盘内。 (Ⅵ) 具奇异摄动离散时滞广义系统的鲁棒稳定性判据 给出了一类具奇异摄动离散多时滞广义系统的鲁棒稳定性判据，该判据给更多还原

【Abstract】 With the rapid development of the computer techniques, the subject of discrete systems has recently received much attention in the fields of engineering, control and science. This dissertation, which is made up of seven parts, focuses on the robust stability and control of discrete singular systems with delay.In section Ⅰ, the general solution, local reachability and local controllability is discussed for discrete singular systems with delay and without delay. First, by Z-transform, the general solution is derived for discrete singular systems with delay and without delay, next, necessary and sufficient conditions are established for local reachability and local controllability. At last, a numerical example is presented.Section Ⅱ analyzes qualitatively and quantitatively discrete singular systems with delay and quadratic delay. Firstly, it discusses qualitatively and quantitatively discrete system with delay and quadratic delay by Lyapunov’s method , and estimates the sizes of the uniform stability region and asymptotic stability region for the systems. Secondly, for a sufficiently small delay, uniform stability and asymptotic stability is obtained for discrete singular systems with the delay. Finally, an important problem of the maximum stability region is proposed.Section Ⅲ investigates the stability and robust stability for discrete singular systems with multiple delays. Firstly, two asymptotic stability criteria are established for discrete singular systems with multiple delays. One is a direct test and another is a boundary test. Secondly, an simple robustness stability criterion independent of delays is derived and the effective quantitative measures is provided for robust stability and performance robustness of discrete uncertain singular systems with multiple delays.Section Ⅳ investigates the robustness for pole assignment of discrete uncertain singular systems with multiple delays, and presents sufficient criteria , that is all the limited poles of discrete uncertain singular systems with multiple delays lie in certain specified regions. No restriction is imposed on the shapes of the specified regions.更多还原