Closeness of Solutions for Singularly Perturbed Systems via Averaging
Provides theoretical guarantees for averaging in singularly perturbed systems with non-equilibrium boundary layers, relevant for control and dynamical systems theory.
The paper studies singularly perturbed nonlinear differential equations and proves that solutions of the full system are O(√ε)-close to those of the reduced average and boundary layer systems over finite time, under assumptions that boundary layer solutions converge to a bounded set.
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(\sqrt(ε)), where εis the perturbation parameter.