ON PERIODIC ORBITS OF 3D SYMMETRIC PIECEWISE LINEAR SYSTEMS WITH REAL TRIPLE EIGENVALUES

The counter-intuitive appearance of stable periodic orbits in three-dimensional piecewise linear systems has been recently reported for stable saturated control systems with high gain and real triple eigenvalues [Moreno & Suárez 2004]. In this letter using several mathematical tools, the reported sudden phenomenon is explained, and the analysis is completed by providing a global bifurcation diagram of the symmetric periodic orbits. Approximate methods are used only to illustrate the nonlinear behavior with respect to the bifurcation parameter. Analytical methods are employed to rigorously prove the main result. The employed techniques are useful not only for the family studied but also for generic three-dimensional symmetric piecewise linear systems.