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.

Keywords

• roughness
• controllability
• impulsive semilinear evolution equation
• delay
• nonlocal conditions
• rothe’s fixed point theorem
• primary 34k35
• secondary 37l05