Controllability of nonlinear fractional delay dynamical systems with prescribed controls

摘要

In this paper, we consider controllability of nonlinear fractional delay dynamicalsystems with prescribed controls. We firstly give the solution representation of the fractional delaydynamical systems using Laplace transform and Mittag–Leffler functions. Then we give necessaryand sufficient conditions for the controllability criteria of linear fractional delay dynamical systemswith prescribed controls. Further, we use a fixed point theorem to establish the sufficient conditionfor the controllability of nonlinear fractional delay dynamical systems with prescribed controls.In particular, we determine several sufficient conditions on the nonlinear function term so that ifthe linear system is controllable, then the nonlinear system is controllable. Finally, we give twoexamples to demonstrate the applicability of our obtained results.