Lyapunov Approach for Stability of Integro-Differential Equations with Non Instantaneous Impulse Effect
Authors :
Anju Sooda,* and Sanjay K. Srivastava b
Author Address :
aDepartment Applied Sciences, Discipline: Mathematics, Punjab Technical University, Kapurthala-144601, India.
bDepartment Applied Sciences, Discipline: Mathematics, Beant College of Engineering and Technology, Gurdaspur-143521, India.
*Corresponding author.
Abstract :
In this paper an integro-differential system of equations, with fixed moments of non instantaneous impulse effects is considered. Sufficient conditions for stability and asymptotic stability of this system have been worked out. The investigations are carried out by means of piecewise continuous functions, analogous to Lyapunov functions and by means of the theory of differential inequalities for such functions. A new comparison lemma, connecting the solution of the given impulsive integro-differential system to the solution of a scalar impulsive differential system is also established.
Keywords :
Impulsive integro-differential systems, non instantaneous impulses, Lyapunov stability, asymptotic stability, Lyapunov function.
DOI :
Article Info :
Received : September 11, 2015; Accepted : October 27, 2015.
