Stability Analysis Of Several Classes Of Control Systems With Time Delay

At present,time delay system has roused much concern.The research on the time delay system is inseparable from the stability analysis.Stability is one of the basic structural characteristics of the system.For one thing,time delay may cause system instability.For another,the performance of the system is usually weakened or damaged due to time delay.The stability of the system is an important condition for the well-balanced operation of the system.The performance of the system can be better studied only if the system is stable.The modern system theory also includes the study of system stability theory.Based on Lyapunov stability theory,we mainly analyzes the asymptotic stability of additive time delay systems.For system stability,we obtain a sufficient condition.First of all,we consider the new Lyapunov functional,and reduce the conservatism of the conclusion.Secondly,in the derivation,this paper adopt the properties of Jensen inequality,linear matrix inequalities and convex polyhedron method.Finally,the validity of data simulation and image simulation to show the conclusions.In this paper,the way used in the process is uncomplicated and easily to understand.The stability criterion is general and be able to suitable for use a wider extent and with less state variables.The thesis is divided into five chapters.The main results are as follows:1.This paper describes the research background and the present situation of the time delay control system,and the researching content of this paper.2.In this paper,Lyapunov stability theory are given.3.The stability of time delay systems with two additive delays is analyzed.In the study,we construct a novel Lyapunov functional,the stability of the system are less conservative results according to the method of convex polyhedron.The outcome of this text can be spread to systems with several delays.At last,four cases are served to show the validity of the presented way through data simulation and image simulation.4.The asymptotic stability with time delay systems is researched.In the study,considering a novel Lyapunov functional,the whole interval is divided into a plurality of inter cell,in the upper bound calculation of the derivative,we introduce different slack variables relative to each cell for the sake of get more rigorous upper bound.The stability of the system are less conservative results.Finally,the case is served to showthe feasible of the presented way through data simulation.5.Finally,the full text of the summary and expectation.