PWL approximation of nonlinear dynamical systems, Part--I: structural stability

This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)