Controllability of fractional-order damped systems with time-varying delays in control
Bin-bin HE1(), Hua-cheng ZHOU2(), Chun-hai KOU3()
1. College of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China 2. School of Mathematics and Statistics, Central South University, Changsha 410075, China 3. Department of Applied Mathematics, Donghua University, Shanghai 201620, China
In this study, we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control. For the linear system based on the Mittag-Leffler matrix function, we define a controllability Gramian matrix, which is useful in judging whether the system is controllable or not. Furthermore, in two special cases, we present serval equivalent controllable conditions which are easy to verify. For the nonlinear system, under the controllability of its corresponding linear system, we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable. Finally, two examples are given to illustrate the theory.
