Discretization behaviors of equivalent control based sliding-mode control systems with external disturbances

In this paper, we study discretization behaviors of the equivalent control based sliding-mode control (SMC) systems. According to the variation of system parameters, the inherent dynamical behavior of the trajectories within some specified boundaries are discussed. Also upper bounds for the system steady states using symbolic dynamics approach are established. Some dynamical properties of the discretized second-order systems under the existence of uncertainties and disturbances are first explored. This paper include upper bounds for this system's steady states and steady state behaviors, which has not been addressed before. Simulations are presented to verify the theoretical results.