Relative approximate controllability of abstract functional systems with infinite delay and delayed control

This paper is concerned with the relative approximate controllability of functional systems with infinite delay and delayed control in Hilbert spaces. In particular, we begin with studying some criteria of the controllability of linear systems. Based on those results, sufficient conditions are derived for the relative approximate controllability of nonlinear functional systems. Finally, an example is included to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.