Controllability of time-delay fractional systems with and without constraints

摘要

This study presents time-delay linear fractional systems with multiple delays in control. The formula for a solution of the discussed systems is presented and derived with the use of the Laplace transform. The definitions of controllability for time-delay fractional systems with and without constraints are introduced. Constraints are imposed on control values. New criteria for relative controllability and relative U-controllability for fractional systems with delays in control are established and proved. The obtained results are illustrated with numerical examples.