Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems

• A fractional order PID controller is designed.
• Fractional delay systems with commensurate orders and multiple commensurate delays are studied.
• The time delays in the system may belong to several distinct intervals.
• The D-subdivision method is employed to choose the stabilizing set of the controller parameters.
• The mean value of the obtained stabilizing set is selected to design a non-fragile controller.

A fractional order PID controller is designed to stabilize fractional delay systems with commensurate orders and multiple commensurate delays, where the time delays in the system may belong to several distinct intervals. Moreover, the controller parameters should belong to given intervals. In order to stabilize the system, the D-subdivision method is employed to choose the stabilizing set of the controller parameters from their available values. Furthermore, the nearest values of the obtained stabilizing set to their mean values are selected as the controller parameters so that a non-fragile controller is concluded. Two numerical examples evaluate the proposed control design method.