The dynamical behaviors of an Euler discretized slidingmode
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.