Approximate controllability of non-instantaneous impulsive semilineartime-dependent control systems with unbounded delay and non-local condition

Abstract

In this work, we study the approximate controllability of a control system with unbounded delay, non-instantaneous impulse, and non-local conditions. These results prove once again that the controllability of a linear system is preserved if we consider theimpulses, the non-local conditions and the delays as disturbances of it, which is very natural in real life problems, never the critical points of a differential equation is exactly the critical point of the model that it represents, the same happens withthe impulses, the delay and non-local conditions; they are intrinsic phenomena to the real problem, that many times they are not taken into account at the moment of carrying out the mathematical modeling. To achieve our result, we will use a technique developed by A. Bashirov et al., which does not use fixed point theorems. On the other hand, as the delay is infinite, we consider a phase space that satisfies the axiomatic theory propose by Hale-Kato to study retarded differential equations with unbounded delay.

Keywords

• approximate controllability
• bashirov et. at technique
• hale-kato axiomatic theory
• non-instantaneous impulses
• non-local conditions
• semilinear retarded equations with infinite delay