Estimating the region of attraction on fractional-order complex networks with time-varying delay

Abstract

Recently, there has been increasing attention towards reckoning the region of attraction (ROA) for networks. However, applying existing theory to networks with fractional-order and delays presents significant challenges. This article addresses the estimation of ROA for fractional-order complex networks with time-varying delay. Initially, two generalized fractional-order Halanay inequalities are formulated. Subsequently, leveraging the first Halanay inequality, a method for ROA estimation is developed, which is unaffected by both delay and fractional-order. However, this method tends to be conservative. To mitigate this conservatism, a delay-dependent and order-dependent ROA estimation technique is proposed based on our two developed Halanay inequalities. Additionally, numerical examples are presented to validate the proposed methodologies.