Some Results on Controllability and Observability of Finite-dimensional Fractional Differential Systems

Abstract

In this paper, some structural results of main concern for control theory are given for finite-dimensional linear fractional differential systems. The controllability and observability properties of such systems, given either in state-space form or in polynomial representation, are closely defined, and then carefully solved from an analytic point of view. The results are then restated in an algebraic form, which happily proves to be the same as for finite-dimensional linear ordinary differential systems. 1. INTRODUCTION Fractional differential systems have proved to be useful in control processing for the last two decades (see [14, 15]). Although the notion of fractional derivative dates back two centuries, several authors have recently published reference books on the subject: see [17] for a thorough mathematical study, and [11] for a treatment of linear fractional differential equations. The question of stability is of main interest in control theory; it has been addressed in [2,...