Discretization behaviors of equivalent control based sliding-mode control systems

In this note, discretization behaviors of the equivalent control based sliding-mode control (SMC) systems are studied. Some inherent dynamical properties of the discretized second-order systems are first explored. Upper bounds for the system steady states are established. The system's steady-state behaviors are discussed. The analysis for the second-order systems is then extended to higher order systems. Simulations are presented to verify the theoretical results.