Conference Proceedings

Closeness of Solutions for Singularly Perturbed Systems via Averaging

Mohammad Deghat, Saeed Ahmadizadeh, Dragan Nesic, Chris Manzie

Proceedings of the ... IEEE Conference on Decision & Control / IEEE Control Systems Society. IEEE Conference on Decision & Control | IEEE | Published : 2018

Abstract

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O (√{ε}), where ε is the perturbation parameter.