New Controllability Criteria for Fractional Systems with Varying Delays

Abstract

Finite-dimensional dynamical control systems described by linear fractional-order state equations with multiple delays in control varying in time are presented in the paper. Both the unconstrained and constrained controls are considered. The constraints are put on the control values. The set of admissible control values is assumed to be a convex and compact set containing 0 in its interior and a cone with vertex at zero and a nonempty interior. New necessary and sufficient conditions for unconstrained as well as for constrained relative controllability of fractional-order systems with delayed varying controls are established and proved. A numerical example is presented to illustrate the obtained theoretical results.