Positive Edge-Consensus of Uncertain Fractional-Order Networked Systems

This paper addresses the edge-consensus problem in a directed nodal network, where each edge is described by uncertain fractional-order dynamics subject to positivity constraints. To solve the issues of positivity and consensus in uncertain fractional-order networked systems (UFONSs) with the order 0 < <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> ≤ 1, a distributed control protocol by virtue of state feedback is designed. Some sufficient criteria are established to ensure positive edge-consensus of UFONSs. Subsequently, to handle scenarios with unmeasurable states in practical systems, an observer-based control protocol is proposed to achieve positive edge-consensus for UFONSs. Furthermore, by leveraging the fractional-order stability theory and the properties of positive systems, some sufficient positive edge-consensus conditions that depend only on the number of edges and nodes are formulated instead of the global information of the network. Finally, two simulation examples are shown to verify the feasibility of the proposed protocols.