Title: Null controllability of semilinear delay control systems

Authors: Suman Kumar

Addresses: Department of Mathematics, IGNTU Amarkantak, Madhya Pradesh, India

Abstract: In this paper, the null controllability results for a class of semilinear delay control systems have been established. The fundamental semigroup is generated by using the perturbation due to the linear delay operator, which defines the fundamental solution of the system. Then, the null controllability of the associated linear delay control system has been deduced assuming that the linear non-delay control system is null controllable. The sufficient conditions have been introduced to establish the null controllability of semilinear delay control systems. The main result is proved by applying the Krasnoselskii fixed point theorem. The application of the derived result is demonstrated by a parabolic partial differential equation of diffusion process.

Keywords: null controllability; delay differential systems; fundamental solution; semilinear control systems.

DOI: 10.1504/IJDSDE.2024.144888

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.4, pp.412 - 425

Received: 16 Jul 2024
Accepted: 13 Dec 2024
Published online: 06 Mar 2025 *