H-infinity consensus control of fractional-order multi-agent systems

Abstract

This paper considers the H-infinity consensus problem of fractional-order multi-agent systems (FOMASs) with external disturbances ( 0 < α < 1 ). Using matrix spectral decomposition and the algebra properties of the Kronecker product, the H-infinity consensus problem in FOMASs is converted to an H-infinity problem for a group of fractional-order systems (FOSs). Based on the bounded real lemma of H-infinity stability for FOS in term of linear matrix inequalities (LMIs), a necessary and sufficient condition for the existence of an H-infinity controller achieving consensus in FOMASs is derived. A multi-step procedure for constructing controller is further presented. In the simulation part of the paper, the viability of the proposed method is demonstrated by a simulation example. A comparative analysis of the performance of controllers designed based on integer-order models and fractional-order models is subsequently conducted to elucidate the distinct advantages of method in this paper.