Controllability of Fractional Differential Systems with State and Control Delay by Using Riemann--Liouville Fractional Derivatives - Ghandor, Wadii; Aberqi, Ahmed; Ech-chaffani, Zoubida; Karite, Touria (Discontinuity, Nonlinearity, and Complexity, 2026)
This paper investigates the controllability of linear fractional-order control systems featuring both state and control delays, using the Riemann-Liouville fractional derivative framework. An explicit representation of the system's solution is derived, enabling the formulation of a controllability criterion based on the rank condition. We establish necessary and sufficient conditions ensuring controllability of the considered class of fractional systems. To validate the theoretical results, a numerical example is provided and discussed. In particular, a numerical simulation is carried out to illustrate the behavior of the system under the designed control law. The evolution of the state trajectories and the applied control input are plotted, showing the impact of the delay and the fractional-order dynamics on the system performance.