Study On Stability Domains Of A Kind Of Difference Equations

The nature of the stability problems is to study the influence of the interference to the motion state of the system, but in practical problems, the interference is unavoidable. The stability domain problems are to resolve how restricts the starting area of the solutions of the system, and then it possibly reduces the impact of interference to the system, obtaining the desired results. The method studying on the stability and stability domain is Lyapunov stability theory, the core part of the stability theory is Lyapunov second method, called Lyapunov direct method, it is the main method of system stability research. Lyapunov direct method does not solve the solution of the system, while by constructing appropriate Lyapunov function, determines the system stability and its stability domain and its estimation. Over recent years, many scholars do not construct the Lyapunov function, but consider the equations themselves, scholars find the conditions to satisfy system stability.This paper mainly studies stability of a kind of difference equations and its stability domains estimation. Firstly, based on the existing stability theorems of the differential equations, by Lyapunov direct method, it constructs the difference of a continuous function and Lyapunov function for determining stability of the difference equations, thus the stability theorems are improved and expanded; Secondly, by the method constructing Lyapunov function, the stability theory of quadratic delay difference systems and its stability domain estimation are given, where dealing with the delay values, it requires delay values are the admissible values range under conditions; Thirdly, the method used to discuss asymptotic stability domains of autonomous difference equations by constructing Lyapunov functions is applied to discuss the uniform asymptotical stability domains of non-autonomous difference systems. And this paper improves the conclusion determining asymptotical stability domains of autonomous difference equations, popularizes the application range of the conclusion.