Finiteness conditions for performance indices in generalized fractional-order systems defined based on the regularized Prabhakar derivative

In the present paper, we introduce the generalized fractional-order control systems with the regularized Prabhakar fractional derivative and investigate the BIBO stability for this kind of systems. For such kind of systems with step functions at their inputs, we establish some conditions imposed on the parameters of the corresponding fractional-order transfer functions under which the steady state error is zero and the performance indices are finite. Further, in order to examine the analytical obtained results, several generalized fractional-order transfer functions are considered. Then, we show that the parameters of the regularized Prabhakar fractional derivative play significant roles in finiteness of the performance indices in the systems.