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

In this paper, we utilize a diagonally dominant structure for the decentralized stabilization of unknown nonlinear time-delayed networks. Generalizing the idea of virtual contraction analysis to time-delayed systems, we demonstrate that nonlinear time-delayed networks can be stabilized by diagonal high-gains if the input matrices possess certain generalized (column/row) diagonally dominant properties. To achieve stabilization of unknown networks, we further propose a distributed adaptive tuning rule for each individual gain function, ensuring that all closed-loop trajectories converge to the origin. The effectiveness of the proposed decentralized adaptive control is verified in a case study on epidemic spreading control in SIS networks with transmission delays.