Virtual Contraction Approach to Decentralized Adaptive Stabilization of Nonlinear Time-Delayed Networks

In this paper, we exploit a diagonally dominant structure for the decentralized stabilization of unknown nonlinear time-delayed networks. To this end, we first introduce a novel generalization of virtual contraction analysis to diagonally dominant time-delayed control systems. We then show that nonlinear time-delayed networks can be stabilized using diagonal high-gains, provided that the input matrices satisfy certain generalized (column/row) diagonally dominant conditions. To enable stabilization of unknown networks, we further propose a distributed adaptive tuning rule for each individual gain function, guaranteeing that all closed-loop trajectories converge to the origin while the gains converge to finite values. The effectiveness of the proposed decentralized adaptive control is illustrated through a case study on epidemic spreading control in SIS networks with transmission delays.