Approximate controllability of impulsive semilinear stochastic system with delay in state

ABSTRACT

Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process that can be modeled by impulsive differential equations. This article studies the approximate controllability of impulsive semilinear stochastic system with delay in state in Hilbert spaces. Assuming the conditions for the approximate controllability of the corresponding deterministic linear system, we obtain the sufficient conditions for the approximate controllability of the impulsive semilinear stochastic system with delay in state. The results are obtained by using Banach fixed point theorem. Finally, two examples are given to illustrate the developed theory.

KEYWORDS:

• Approximate controllability
• semilinear systems
• impulsive stochastic system
• state delay

MATHEMATICS SUBJECT CLASSIFICATION:

• 93B05
• 93C10

Funding

U. Arora is thankful to Ministry of Human Resource Development (Grant code: MHR-02-23-200-304) for their financial support to carry out her research work.