In this paper, dynamical behaviors of the discretetime
sliding-mode-control (DSMC) uncertain systems are studied.
First, a discrete reaching law with a disturbance compensator
is presented, and a sliding-mode controller is designed by using
the proposed reaching law. Second, the time steps for the system
trajectories to converge to the switching manifold are found. Then,
a quasi-sliding-mode domain (QSMD) of the DSMC uncertain systems
is obtained, and the system dynamics of the DSMC systems
in QSMD are described. Finally, numerical simulations are given
to demonstrate the effectiveness of the proposed strategies.