Volume 2, Issue 3, March 2013, Pages 280–286
Sanjay K. Srivastava1 and Kanwalpreet Kaur2
1 Department of Applied Sciences, Beant College of Engineering and Technology, Gurdaspur-143521, Punjab, India
2 Department of Applied Sciences, C.T. Institute of Technology, Jalandhar-144020, Punjab, India
Original language: English
Copyright © 2013 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, the stability of general impulsive retarded functional differential equations with any time delay has been considered. Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. Impulsive differential equations, that is, differential equations involving impulse effects, are a natural description of observed evolution phenomena of several real world problems. Impulsive control which based on impulsive differential equations has attracted the interest of many researchers recently. The method of Lyapunov functions and Razumikhin technique have been widely applied to stability analysis of various delay differential equation. When Lyapunov functions are used, it becomes necessary to choose an appropriate minimal class of functionals relative to which the derivative of the Lyapunov function is estimated. This approach is known as the Lyapunov
Author Keywords: Impulsive delay systems, Lyapunov function, Razumikhin technique, Uniform stability, Time delays.
Sanjay K. Srivastava1 and Kanwalpreet Kaur2
1 Department of Applied Sciences, Beant College of Engineering and Technology, Gurdaspur-143521, Punjab, India
2 Department of Applied Sciences, C.T. Institute of Technology, Jalandhar-144020, Punjab, India
Original language: English
Copyright © 2013 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, the stability of general impulsive retarded functional differential equations with any time delay has been considered. Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. Impulsive differential equations, that is, differential equations involving impulse effects, are a natural description of observed evolution phenomena of several real world problems. Impulsive control which based on impulsive differential equations has attracted the interest of many researchers recently. The method of Lyapunov functions and Razumikhin technique have been widely applied to stability analysis of various delay differential equation. When Lyapunov functions are used, it becomes necessary to choose an appropriate minimal class of functionals relative to which the derivative of the Lyapunov function is estimated. This approach is known as the Lyapunov
Author Keywords: Impulsive delay systems, Lyapunov function, Razumikhin technique, Uniform stability, Time delays.
How to Cite this Article
Sanjay K. Srivastava and Kanwalpreet Kaur, “Stability of Impulsive Differential Equation with any Time Delay,” International Journal of Innovation and Applied Studies, vol. 2, no. 3, pp. 280–286, March 2013.
