Abstract
In this paper, firstly a new class of time-delay differential inequality is proved. Then as an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the trivial solution of the nonlinear systems with multiple delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variables. It is obvious that the above system is a generalization of the traditional differential systems. The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria. As a result, the partial stability of differential equations is widely used both in theory and in practice such as dynamic systems and control systems.
Highlights
In 1892, Lyapunov, a Russian mathematician, mechanician and physicist, proposed the notion of the stability of motion
As an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the trivial solution of the nonlinear systems with multiple delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variables
The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability
Summary
In 1892, Lyapunov, a Russian mathematician, mechanician and physicist, proposed the notion of the stability of motion He gave the general research methods in his doctoral dissertation “The general problem of the stability of motion” [1], in which he established the foundation of the stability theory. As a result, studying the partial stability of differential equations becomes more important. It is of practical significance to study the partial stability of differential equations. In 1986, Dannan and Elaydi ([2]) introduced a new notion of stability, which is called uniform Lipschitz stability (ULS), for systems of differential equations dx dt. The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria
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