Stability Analysis Of Time-delay Systems Based On Improved Integral Inequality

It is well known that the existence of time delay leads to deterioration of system's performance or instability.In many years,the study of the stability analysis of time-delay system is of critical importance in the systematic theory field.It has also aroused extensive concern by many scholars.In this thesis,the stability of two types of time-delay systems is analyzed and sufficient conditions to determine the system's stability are obtained.The main contents are as follows:Firstly,an improved double integral inequality is derived by using free-weighti ng-matrix technique and some inequality lemma.Compared with the Wirtinger-base d double integral,this new inequality can be less conservative both in practical an d theoretical fields.Secondly,In order to analyze the stability of linear systems with neutral and distributed delays,an appropriate Lyapunov-Krasovskii(L-K)function is constructed and this newly proposed double integral inequality is employed.Better sufficient conditions are thus obtained for the stability test.Numerical examples are given to demonstrate its effectiveness.The calculations show that the upper bound of the maximum time-delay obtained by our method is bigger than those by previous methods.This verifies that the results applying this new inequality can reduce the conservatism effectively.Our theoretical research has certain significance to improve the ways of stability analysis for time-delay systems.Finally,we summarize the stability analysis on these two kinds of time-delay systems and propose some future research based on the present study.