Stability and Robustness Analysis of Commensurate Fractional-Order Networks

Abstract

Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient condition for the stability of networks of cyclic interconnection of fractional-order systems when the digraph describing the network conforms to a single circuit. The condition becomes necessary under a special situation where coupling weights are uniform. We then investigate the robustness of fractional-order linear networks. Robustness performance of a fractional-order linear network is quantified using the $\mathcal H_2$ -norm of the dynamical system. The theoretical results are confirmed via some numerical illustrations.