Stability Analysis And Control Of Additive Time-delay Systems Based On LMI

The time-delay usually affects the system performance and destroys its stability.Therefore,it is necessary to analyze the stability of time-delay systems in order to reduce the influence of time-delay factors.At present,a lot of achievements have been made in the study of the stability of time-delay systems.However,in many systems,affected by various internal and external factors,a time-delay system which contains several timedelay components with different characteristics is called additive time-delay system.Many researches have not subdivided the time-delay of the system,but because the characteristics of these time-delay components are different,it is necessary to study them separately.In the study of additive time-delay systems,for convenience,we usually study the case with two time-delay components,and then generalize to the case with multiple time-delay components.The study process is based on considering the two components separately,and the maximum admissible upper bound of the system is the sum of the maximum values of the two components.This is different from the case where all timedelay components are considered as a unified whole.Considering the different characteristics of the two time-delay components,it is usually more accurate to study the two time-delay components separately to obtain the maximum admissible upper bound of the delay,in order to achieve more accurate control of the system.In this paper,we mainly study the stability of additive time-varying delay systems in the following three aspects,and give some conclusions in the form of Linear Matrix Inequality Group(LMIs):(1)Analyzing the stability of a class of additive time-varying delay systems with two time-delay components.A new Lyapunov-Krasovskii(L-K)functional is established,in which the information of two time-varying delay components is fully considered by using integral term,and the delay information is further considered by using triple integrals to reduce the conservativeness of the system.The stability of the system is analyzed by using Jensen integral inequality and reciprocally convex matrix inequality correlation method.The conclusion of stability with less conservativeness is obtained.Then,based on the stability of the nominal system,the robust stability and the H_? stability theorem are obtained.(2)In the case of nonlinear systems,the stability of a class of T-S fuzzy systems with two additive time-delay components is studied.By using the Free-matrix-based integral inequality,a less conservativeness stability conclusion of T-S systems with additive timedelays is obtained.The conservativeness of the stability criteria obtained by this method can be obviously reduced.(3)A class of network control systems with both state delay and additive network time-delay components are considered,and the controller is designed.In the case of disturbance,the stability problem of T-S fuzzy systems with additive time-delay is studied and the stabilization is analyzed.In this part,a new L-K functional is constructed,which combines the Free-matrix-based integral inequality with the Jensen's inequality method,considering the validity of the methods used in the first two parts and the principle of simplicity in computation,the stability controller of T-S fuzzy networked control systems with additive time-delay is designed.