Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions

Abstract

In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe’s fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.

Keywords

• exact controllability
• semilinear time varying control systems
• non-instantaneous impulses
• delay
• nonlocal conditions
• rothe’s fixed point theorem