Trajectory-Based Region of Attraction Estimation on Higher-Order Networked Nonlinear Systems

This letter presents a theoretical framework for estimating the trajectory-based region of attraction in nonlinear higher-order networks. A Lyapunov-based criterion is established for time-varying systems to determine the domain in which all trajectories converge to a reference trajectory. The result is expressed as a spherical region characterized by parameters of the linearized dynamics. Two corollaries admit closed-form and eigenmode-based estimations, respectively enabling a direct region radius calculation and reducing system dimension significantly. Numerical simulations on a higher-order network of forced pendulums validate the proposed analysis and demonstrate its accuracy and efficiency.