Approximation of large-scaled dynamical systems based on multi-layered hierarchical structure and multiple time scales

In this paper, we deal with approximation methods of large-scaled complex systems and derive the condition that the equilibrium point of the error dynamics is exponentially stable. Especially, we propose multi-layered hierarchical model which approximates the large-scaled systems. Our heterogeneous approximation is preferable for preserving the details of a subsystem of our interest and simplifying the other parts of such large-scaled systems. Finally, numerical simulations are demonstrated to show the efficiency.