Singular perturbation in piecewise-linear systems.

A singular perturbation technique is developed which allows for a decoupling of a continuous piecewise-linear system into slow and fast subsystems. Under the assumption of asymptotic stability, the fast variable is found to decay in the boundary layer to its quasi-steady-state solution. This quasi-steady-state solution is given by a continuous implicit function of the slow variable. The solution is found using the finite-step algorithm given in the paper. Sufficient conditions for the approximation to the accurate to an order of O(μ) are given, where μ is a parameter related to the expanded time scale.