The Implicit Discretization of the Supertwisting Sliding-Mode Control Algorithm

• Published in: IEEE transactions on automatic control Vol. 65; no. 8; pp. 3707 - 3713
• Main Authors: Brogliato, Bernard, Polyakov, Andrey, Efimov, Denis
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Asymptotic stability; Closed loop systems; Computer simulation; Continuous time systems; Control algorithms; Control theory; Discrete time systems; Discretization; Feedback control; Implicit Euler discretization; Level set; Liapunov functions; Lyapunov methods; Lyapunov stability; Numerical stability; Sliding mode control; Stability analysis; supertwisting algorithm
• ISSN: 0018-9286; 1558-2523; 2334-3303; 1558-2523
• DOI: 10.1109/TAC.2019.2953091

This article deals with the analysis of the time discretization of the supertwisting algorithm, with an implicit Euler method. It is shown that the discretized system is well posed. The existence of a Lyapunov function with convex level sets is proved for the continuous-time closed-loop system. Then, the global asymptotic Lyapunov stability of the unperturbed discrete-time closed-loop system is proved. The convergence to the origin in a finite number of steps is proved also in the unperturbed case. Numerical simulations demonstrate the superiority of the implicit method with respect to an explicit discretization with significant chattering reduction.