Stability And Robust Stability Analysis Of A Class Of Integral Delay Systems

Among the field of electric, medical science and biochemistry, time delay is a general question. To describe the problems more accurately, the differential equations that conclude time delays are catching increasingly attentions. This paper mainly discusses about the stability and robust stability of a class of integral delay system, including a class of stability theorem, a necessary condition for the system’s exponential stability, methods for numerical solutions and its applications in neutral stochastic differential equations.First of all, a Lyapunov theorem which can prove the system’s exponential stability is introduced according to the theorem for general systems. A Lyapunov function is proposed and by contracting the inequalities, a class of necessary condition for the system’s exponential stability is established.Next, different cases of perturbation are considered based on the former Lyapunov theorem and the system’s robust stability is analyzed in the following part. A Lyapunov function is proposed and the robust stability theorem is established and proved.In addition, this paper offer a numerical example to prove the effectiveness of the results obtained, and bring forward a method to prove the system’s stability according to the necessary condition. By obtaining the range of the delayed time, the conclusion of the paper is verified. The conclusion is also proved to be less conservation comparing to the existing conclusion.At last, as an application of the integral time-delay system, the paper discusses the situation when the integral delay system is used into the neutral stochastic differential equations with delays and Brownian motion. The stability of this class of system is closely related to the integral time delay system. By using the Lyapunov stability conditions of the integral time delay system, a group of conditions for the exponential stability in mean square is established.