In this paper we extend the classical high gain theorem to linear fractional systems of commensurate order. The main purpose of the present work is to stabilize this special class of fractional order systems using a high gain output feedback. The basis for extending this theorem lies in the stability results derived by Matignon. The derived theorem ensures the stabilization of linear fractional systems of arbitrary commensurate order under certain assumptions. A numerical example illustrates the effectiveness of the approach. Furthermore, We employ the Particle Swarm Optimization (PSO) algorithm to tune the high gain feedback so that the output of the closed-loop system reaches a desired value. The study provides valuable insights for linear fractional order systems of commensurate order.
Boudana et al. (Wed,) studied this question.