Total controllability of non-autonomous second-order measure evolution systems with state-dependent delay and non-instantaneous impulses

Abstract

This paper investigates a new class of non-autonomous second-order measure evolution systems involving state-dependent delay and non-instantaneous impulses. We introduce a stronger concept of exact controllability called total controllability. The existence of mild solutions and controllability for the considered system are obtained by applying strongly continuous cosine family and the Mönch fixed point theorem. Finally, an example is used to verify the practical application of the conclusion.

Keywords

• mönch fixed point theorem
• second-order evolution systems
• state-dependent delay
• non-instantaneous impulses
• total controllability