Study of Periodic Solutions in Discretized Two-Dimensional Sliding-Mode Control Systems

The existence of periodic solutions in discretized 2-D equivalent control-based sliding-mode control systems is studied. Admissibility conditions for the existence of periodic solutions with specific symbol sequences are derived, and admissibility regions for short periodic sequences are found. It is shown that, for certain parameter values, there exist arbitrarily long periodic orbits for arbitrarily small discretization steps. Theoretical results are illustrated with simulation examples.