Stability results for fractional differential equations with applications to control processing

Abstract

In this paper, stability results of main concern for control theory are given for finite-dimensional linear fractional differential systems. For fractional differential systems in state-space form, both internal and external stabilities are investigated. For fractional differential systems in polynomial representation, external stability is thoroughly examined. Our main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector jarg(oe)j ff=2, thus generalizing in a stupendous way the well-known results for the integer case ff = 1. 1. INTRODUCTION Fractional differential systems have proved to be useful in control processing for the last two decades (see [21, 22]). The notion of fractional derivative dates back two centuries; some references that have now become classical were written two decades ago (see [20, 25]). Several authors published reference books on the subject very recently: see [26] for a thorough mathem...