Stability and Robustness Analysis of Commensurate Fractional-order Networks

TL;DR

This paper extends stability analysis to cyclic interconnected commensurate fractional-order networks, providing new conditions for stability and robustness, with numerical validation demonstrating practical applicability.

Contribution

It introduces a generalized secant condition for stability of fractional-order networks with a single circuit digraph and analyzes robustness using the $\\\mathcal{H}_2$-norm.

Findings

Derived a sufficient stability condition for cyclic fractional-order networks.

Identified when the stability condition becomes necessary with uniform coupling.

Quantified robustness of fractional-order networks using the $\mathcal{H}_2$-norm.

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 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. Finally, the theoretical results are confirmed via some numerical illustrations.