Balancing for a class of non-linear singularly perturbed systems

In this work, a balancing method is investigated for a class of non-linear singularly perturbed systems. The main result presented here shows that the well-known ʹtwo-stagesʹ strategy used with singular perturbations in control theory can be extended to compute a balancing form of non-linear singularly perturbed systems. So, an approximate balancing form is derived from the balancing forms of the slow and fast subsystems both computed separately. This two-stage method avoids the difficult task of solving high dimensional and ill-conditioned Hamilton-Jacobi equations due to the presence of the small singular perturbation parameter.