In this work we describe the bifurcation scenario found in a general first order system when a relay based proportional control (sliding-mode control) is considered. Based on the results given in the literature, we show the occurrence of a big bang bifurcation causing the existence of an infinite number of periodic orbits near a co-dimension two bifurcation point. We also extend in a natural way the applied theoretical result for second order systems involving 2D piecewise-defined maps.
- Big bang bifurcations
- Two-dimensional piecewise-defined maps
- Period adding
- Sliding-mode control