Dynamics of controlled linear discrete time systems with a dead-zone nonlinearity

In this work, we study the dynamic behavior of controlled linear discrete time systems with a dead-zone nonlinearity. We show the existence of global bifurcations, such as border collision bifurcations including equilibrium points and periodic orbits, scenarios leading to chaotic attractors, and crisis of chaotic attractors to periodic orbits. Our approach is based on analytical and numerical techniques.