Controllability of semilinear systems with fixed delay in control

Abstract

In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.

Keywords

• first order delay system
• mild solution
• fixed point
• exact controllability