Global Analysis of Piecewise Linear Dynamical Systems ⋆

In this paper, we consider a planar dynamical system with a piecewise linear func-tion containing an arbitrary number of dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system with k dropping sections and 2k + 1 singular points can have at most k + 2 limit cycles, k+1 of which surround the foci one by one and the last, k+2, limit cycle surrounds all of the singular points of this system