80 research outputs found
Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique
This paper develops some new Razumikhin-type theorems on global exponential
stability of impulsive functional differential equations. Some applications
are given to impulsive delay differential equations. Compared with
some existing works, a distinctive feature of this paper is to address exponential
stability problems for any finite delay. It is shown that the functional
differential equations can be globally exponentially stabilized by impulses
even if it may be unstable itself. Two examples verify the effectiveness of
the proposed results
Global exponential stability for coupled systems of neutral delay differential equations
In this paper, a novel class of neutral delay differential equations (NDDEs) is presented. By using the Razumikhin method and Kirchhoff's matrix tree theorem in graph theory, the global exponential stability for such NDDEs is investigated. By constructing an appropriate Lyapunov function, two different kinds of sufficient criteria which ensure the global exponential stability of NDDEs are derived in the form of Lyapunov functions and coefficients of NDDEs, respectively. A numerical example is provided to demonstrate the effectiveness of the theoretical results
Practical Stability of Impulsive Discrete Systems with Time Delays
The purpose of this paper is to investigate the practical stability problem for impulsive discrete systems with time delays. By using Lyapunov functions and the Razumikhin-type technique, some criteria which guarantee the practical stability and uniformly asymptotically practical stability of the addressed systems are provided. Finally, two examples are presented to illustrate the criteria
Exponential Stability of Impulsive Delay Differential Equations
The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are
analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process
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