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Analysis of a Singularly Perturbed Continuous Piecewise Linear System
The dynamics of piecewise linear systems can often be reduced to lower dimensional invariant cones using an appropriate Poincaré map. These invariant cones can be understood as a generalization of the center manifold concept to nonsmooth systems. In this paper, we show that the singular perturbation technique applied to a slow-fast continuous piecewise linear system can deliver a good approximation of the invariant cone. The proposed approximation approach is demonstrated on an oscillator with a unilateral spring as an example of a continuous piecewise linear system in R^3.
