Unified framework for implicit-Euler implementation of second-order sliding mode controllers

Chattering, which mainly occurs by inappropriate discretization, has been one of the significant problems of restricting sliding mode controllers’ practical applications. Toward this problem, this paper presents a unified implicit-Euler discretization framework for the chattering-attenuated implementation of a class of homogeneous second-order sliding mode controllers. The discretization framework calculates a proper value inside the set-valued signum function by considering a particular relation between the current system state and the nonlinear sliding surface. An equivalent relation is employed for mapping an equation containing two cascade set-valued signum functions into an equation including nested project functions. The finite-time convergence and accuracy properties of the proposed framework are analyzed. The results of numerical examples show that the proposed framework significantly attenuates the chattering. It is also shown that the proposed framework provides higher accuracy than the explicit-Euler method.