Summary
For smooth nonlinear systems, available nonlinear order reduction techniques generally require computing the eigenvalues of the underlying linear system. However, the presence of nonsmooth nonlinearities in the dynamics excludes the application of these methods since the system cannot be locally linearized. In this work, we study model order reduction of continuous piecewise linear systems (hereafter, CPWL). We start with a continuous matching method based on the min-max functions and show how singular perturbation reduction can be applied to soft-stiff mechanical systems with CPWL nonlinearity. Finally, we demonstrate how this results in a more general formulation of the invariant cone problem that takes external forcing into account.
