Balancing transformation of nonlinear singularly perturbed systems for model order reduction

This paper is concerned with the methodology of balancing transformation for singularly perturbed systems, which is nonlinear in both the slow and the fast variables. The boundary layer system in introduced and the energy functions are constructed for the slow and fast subsystem respectively. So, an approximate balancing form is investigated in two time scales. It is shown that this method gives accurate measurement to state component and greatly simplifies the process of calculation due to the nonexistence of the small singular perturbation parameter in energy functions.