Compensation Problem in Linear Fractional Order Disturbed Systems

Abstract

In this paper, we study fractional-order linear, finite-dimensional disturbed systems. The fundamental objective of this work is to study the remediability or compensation problem in linear fractional-order time-invariant perturbed systems. The remediability was introduced with the aim of finding an appropriate control that steers the output of the perturbed system towards normal observation at the final moment. We begin first by giving some characterizations of compensation, and then we prove that a rank condition is sufficient to assure the remediability of our system. The relationship between controllability and compensation is also given, and we provide some examples to illustrate our results.