Lyapunov‐based consistent discretization of stable homogeneous systems. (5th November 2020)

• Record Type: Journal Article
• Authors: Sanchez, Tonametl; Polyakov, Andrey; Efimov, Denis
• Other Names: Fridman Leonid guestEditor.; Efimov Denis guestEditor.; Laghrouche Salah guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 31:Number 9(2021)
• Page Start: 3587
• Page End: 3605
• Publication Date: 2020-11-05
• Subjects: discrete‐time systems -- homogeneous systems -- Lyapunov‐based methods -- nonlinear systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5308
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: In this article, we propose a discretization scheme for asymptotically stable homogeneous systems. This scheme exploits the information provided by a homogeneous Lyapunov function of the system. The main features of the scheme are: (1) the discretization method is explicit and; (2) the discrete‐time system preserves the asymptotic stability, the convergence rate, and the Lyapunov function of the original continuous‐time system.