Dynamical behaviours of an Euler discretized sliding mode control systems

The dynamical behaviors of an Euler discretized sliding mode control (SMC) systems based on equivalent control strategy are studied. A periodic-2 orbit in steady state is found for the switching function of the Euler discretized SMC systems. The time steps for the switching function to converge toward the periodic-2 orbit are obtained. When the discretized SMC system is stable, it further shows that the system states of the SMC systems will also enter into some periodic-2 orbits, and these periodic-2 orbits are characterized by explicit analytic expressions. Finally, simulation examples are given to illustrate the theoretical results.