Controllability of second-order nonlocal retarded semilinear systems with delay in control

ABSTRACT

This article is concerned with the second-order nonlocal retarded semilinear differential systems with fixed delay in control. Utilizing the theory of fixed point as well as cosine family, we establish the existence and uniqueness of the mild solution of the system. Then a set of new sufficient conditions are established for the controllability of the semilinear system. The theory is illustrated by providing an example.

COMMUNICATED BY:

• L. Stettner

KEYWORDS:

• Delay system
• strongly continuous cosine family
• mild solution
• fixed point
• controllability

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 93B05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research work is supported by the University Grants Commission, New Delhi, India [grant number 2061440964] during my (first author) stay at IIT Roorkee, Roorkee for the purpose of Ph.D. degree under the supervision of Prof. N. Sukavanam.