This work, led by PhD student Fengyu Yue, investigates the development of a passivity-based framework for analyzing nonlinear consensus dynamics over balanced directed graphs. Although passivity theory is a widely used tool for studying networked dynamical systems, its applicability has traditionally been limited to undirected graphs. This restriction stems from the compositional nature of passivity, which relies on the preservation of passivity properties under symmetric and feedback interconnections. In this work, we begin with the known result that linear consensus over balanced directed graphs behave, asymptotically, in the same way as the undirected setting. We explore the deeper structural reasons why this holds and tie it to notions from passivity theory. We then extend these ideas to more general nonlinear dynamics, requiring us to link notions from submanifold stability theory to passivity-type relations. This work provides an important step towards a broader passivity theory for directed networked systems.
This work was presented at the European Control Conference. It was selected to be included in a special issue of the European Journal of Control. Congratulations Fengyu on the nice work.