The Disturbance Rejection Control of Fractional‐Order System

ABSTRACT This paper studies the problem of disturbance rejection control for fractional‐order systems. Firstly, based on the idea of equivalent input interference and the stability criterion of fractional‐order system, we present sufficient conditions for the disturbance rejection control of fractional‐order system with order , which overcome the limitation that the existing conditions are only sufficient. Secondly, for fractional‐order systems with order , necessary and sufficient conditions for disturbance rejection stabilization of the system are given, and the sufficient condition does not limit the structure of the matrix, which reduces to some extent the conservation of the existing conclusions. Finally, numerical illustrations are reported to show the effectiveness of the results.