The Absolute Stability And Application Of A Class Of Lurie Control System With Multiple Delays And Non-linear Executives

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.