Approximate Controllability of Neutral Stochastic Functional Differential Systems with Infinite Delay

Abstract

In this article, we consider a class of control systems governed by the neutral stochastic functional differential equations with unbounded delay and study the approximate controllability of the system. An example is given to illustrate the result.

Keywords:

• Analytic semigroup
• Approximate controllability
• Hilbert space
• Mild solution
• Neutral stochastic functional differential equation

Mathematics Subject Classification:

• 93B05
• 93E03

The authors wish to thank the referee for the valuable suggestions and comments which resulted in improvement of this paper. Also the first author would like to thank KOSEF fellowship for doing collaborative research work with J. Y. Park, Pusan National University, South Korea during his visit 2005–2006. The work of the third author was supported by UGC-SAP(DRS), Government of India, New Delhi under sanctioned No. F.510/6/DRS/2004(SAP-1).