【作者】 刘目奎；

【导师】 斯力更；

【作者基本信息】 内蒙古师范大学 ， 应用数学， 2004， 硕士

【摘要】 稳定性问题是自动控制系统中的基本问题，它对控制系统的研究有重要的理论意义和实际应用价值。由于任何闭环控制系统都存在滞后效应，所以研究滞后型控制系统的绝对稳定性意义尤为重要。 本文首先推广了Burton T．A．定理，并对文献[1-2]的结果给予补充证明；其次研究了具有多个非线性执行机构的多时滞Lurie系统的绝对稳定性，利用Lyapunov泛函方法，M-矩阵及Burton T．A．定理建立了两个实用的充分条件，推广文献[1-2]的结果，并举例说明结果的有效性；再次讨论了一般非线性时滞控制系统的绝对稳定性，给出判定绝对稳定性的充分条件；最后用同样思想方法讨论了一类带有时滞的飞机纵向运动的绝对稳定性问题，给出一个简易判定的代数充分条件，并将其应用于飞机纵向运动方程，得出较为宽泛简洁的稳定性参数区域估计，推广了有关这方面的研究。 全文共分四章。 第一章：某些定义与引理。主要介绍与本文有关的绝对稳定、M-矩阵的定义及Burton T．A．定理。 第二章：多时滞的Lurie控制系统的绝对稳定。主要介绍利用李雅普诺夫泛函方法，M-矩阵及Burton T．A．定理建立了两个充分性定理，推广了文献[1-2]的结果。 第三章:一般非线性时滞控制系统的绝对稳定性.给出判定绝对稳定性的两个充分条件定理. 第四章:关于带有时滞的飞机纵向运动问题.研究了一类带有时滞的飞机纵向运动系统的绝对稳定性，给出一个简洁的充分条件，且运用到飞机纵向运动方程中去，得到较优越的稳定区域参数估计结果.更多还原

【Abstract】 The stability is a basic problem in automatic control system , which has the significant theoretic and practical application value on the studies of control system . Because the delayed effects exist in any closed- loop control system , it is more important and significant to study the stability of the control system with delay.Firstly, this paper generalizes Burton T.A. theorem and gives a supplementary proof on the results of literatures [1-2]; secondly, the absolute stability of Lurie system with multiple delay and non-linear executive is studied and two practical sufficient conditions are presented by the thread of Lyapunov functional ,M-matrix and Burton T.A. theorem, which popularise the documents [1-2]. A concise example illustrates the effectiveness of the results; thirdly, the absolute stability of the general non-linear control system with delay is discussed and the sufficient conditions are given ; lastly , the absolute stability of a class of plane vertical motion with delay is considered by the same thought and method ,and a concise algebraic sufficient condition is given . The more concise and extensive stability parameter estimation is derived from theresult, which generalizes the relevant studies .This paper consists of four chapters .Chapter one : Definition and lemma. It mainly introduces the definition of absolute stability, M - matrix and Burton T.A. theorem .Chapter two : The absolute stability of Lurie system with multiple delay. The sufficient conditions are set up by means of Lyapunov functional , M-matrix and Burton T.A. theorem ,which popularises the documents[l-2].Chapter three : The absolute stability of the general non-linear control system with delay. Two sufficient criteria are established .Chapter four :On the plane vertical motion with delay .The absolute stability of a class of plane vertical motion with delay is considered and a concise algebraic sufficient condition is given ; especially , the more advantageous stability parameter estimation is derived when the result is applied to the plane vertical motion equation.更多还原