DYNAMICAL COMPLEXITY NEAR NON-CONTROLLABLE 3D PIECEWISE LINEAR LUR'E SYSTEMS

A very useful approach to understand the complex behavior of a system is to consider its degenerate situations. Accordingly the structure of periodic orbits for some degenerate symmetric piecewise linear three-dimensional systems with three zones, whose linear parts share a pair of imaginary eigenvalues is analyzed. Under this hypothesis, the system is noncontrollable and its study can be reduced to the analysis of a periodic one-dimensional equation that can have up to five periodic orbits.