Approximate Controllability of Second-Order Stochastic Distributed Implicit Functional Differential Systems with Infinite Delay

2009 ◽  
Vol 143 (2) ◽  
pp. 225-244 ◽  
Author(s):  
P. Balasubramaniam ◽  
P. Muthukumar
Keyword(s):  
Approximate Controllability ◽  
Infinite Delay ◽  
Second Order ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential

Approximate controllability of semilinear impulsive functional differential systems with non-local conditions

2020 ◽  
Vol 37 (4) ◽  
pp. 1070-1088 ◽  
Author(s):  
Sumit Arora ◽  
Soniya Singh ◽  
Jaydev Dabas ◽  
Manil T Mohan
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Local Conditions ◽  
Functional Differential Systems ◽  
Non Local ◽  
Functional Differential

Abstract This paper is concerned with the approximate controllability of semilinear impulsive functional differential systems in Hilbert spaces with non-local conditions. We establish sufficient conditions for approximate controllability of such systems via resolvent operator and Schauder’s fixed point theorem. An application involving the impulse effect associated with delay and non-local conditions is presented to verify our claimed results.

scholarly journals Impulsive Exponential Stabilization of Functional Differential Systems with Infinite Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
Xiaoli Sun ◽  
Xiaodi Li
Keyword(s):  
Lyapunov Functions ◽  
Infinite Delay ◽  
Exponential Stabilization ◽  
Differential Systems ◽  
Unstable Systems ◽  
Razumikhin Technique ◽  
Numerical Example ◽  
Functional Differential Systems ◽  
Functional Differential

By using the Razumikhin technique and Lyapunov functions, we investigated the impulsive exponential stabilization of functional differential systems with infinite delay. A new result on the exponential stabilization by impulses is gained. Our result shows that impulses can make unstable systems stable. A numerical example is given to illustrate the feasibility of the result.

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