The Euler's discretization effect on sliding mode control of perturbed double integrator

This paper addresses the problem of sliding mode control (SMC) for the perturbed double integrator system. First, the stability conditions of the continuous-time system is analyzed. Moreover, the Euler's discretization of the perturbed double integrator under SMC is introduced and the upper bounds of the discretized system steady states are established. Simulations are presented to illustrate the theoretical results.