Digital implementation of sliding‐mode control via the implicit method: A tutorial

Abstract

SummaryThe objective of this article, is to provide a clear presentation of the discretization of continuous‐time sliding‐mode controllers, also known in the automatic control literature as the emulation method, when the implicit (backward) Euler scheme is used. First‐order, second‐order, and homogeneous controllers are considered. The main theoretical results are recalled in each case, and the focus is put on the discrete‐time implementation structure and on the algorithms which allow the designer to solve, at each time‐step, the one‐step generalized equations which are needed to compute the controllers. The article ends with some open issues.