Trajectory Controllability of Semilinear Systems with Delay in Control and State

In this paper we consider the finite-dimensional dynamical control system described by scalar semilinear ordinary differential state equation with variable delay. The semilinear state equation contains both pure linear part and nonlinear perturbation. We extend the concept of controllability on trajectory controllability for systems with point delay in control and in nonlinear term. Moreover, we present remarks and comments on the relationships between different concepts of controllability. Finally we propose the possible extensions.