Closed trajectories in planar relay feedback systems

摘要

A planar system of piecewise linear differential equations with a line of discontinuity, Z_2―symmetry and a linear part having negative determinant is investigated. Using the theory of differential inclusions and an appropriate Poincare map a complete analysis is provided. This analysis applies to uniqueness and non-uniqueness for the initial value problem, stability of stationary points, sliding motion solutions, number and stability of periodic trajectories and existence of pairs of heteroclinic trajectories connecting two saddle points forming heteroclinic cycles. A complete bifurcation diagram is given.