Relative controllability of nonlinear systems with delays in control

Controllability problems for different types of nonlinear dynamical systems with delays in control has been studied by several authors with the help of different fixed point theorems [1-15]. In particular in the paper [7] the notion of measure of noncompactness of a set and Darbo’s fixed point theorem are used for the study of the relative controllability for nonlinear systems with lumped multiple time varying delays in control and with implicit derivative. The papers [11] and [12] contain sufficient conditions for relative controllability in a given interval for nonlinear dynamical systems with lumped multiple time varying delays in control. The same problems but for nonlinear dynamical systems with distributed delays in control have been discussed and solved in the papers [13] and [14]. Nonlinear dynamical systems with delays in control are the mathematical models of several processes.