Roughness of the Controllability for Time Varying Systems Under the Influence of Impulses, Delay, and Nonlocal Conditions

Abstract

In this paper, we prove that the controllability of time varying linear system is preserved if we add impulses, delay and nonlocal conditions on it. In order to do that, we assume some conditions on the non-linear terms and apply the Rothe’s fixed point theorem to obtain the main result. In other words, we find sufficient controllability conditions for the semilinear system under the influence of impulses, delay, and nonlocal conditions.

Archives of Control Sciences

“…Recently, Leiva et al reported results on controllability considering simultaneously instantaneous impulses, delay and nonlocal conditions using Rothe's fixed point theorem [15]. Motivated by this work and by the work done by Malik, on controllability of nonlocal non-autonomous neutral differential systems including non-instantaneous impulsive effects [16], in this paper, we study the controllability of non-autonomous systems considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously.…”