Controllability of Higher Order Fractional Damped Delay Dynamical Systems with Time Varying Multiple Delays in Control

Abstract

This paper is concerned with the controllability of higher order fractional damped delay dynamical systems with time varying multiple delays in control, which involved Caputo derivatives of any different orders. A necessary and sufficient condition for the controllability of linear fractional damped delay dynamical system is obtained by using the Grammian matrix. Sufficient conditions for controllability of the corresponding nonlinear damped delay dynamical system has established by the successive approximation technique. Examples have provided to verify the results.