A Consistent Discretisation method for Stable Homogeneous Systems based on Lyapunov Function⁎This work was supported by the Agence Nationale de la Recherche project ANR-18-CE40-0008 "DIGITSLID", by the Ministry of Science and Higher Education of Russian Federation, passport of goszadanie no. 2019-0898, and by Government of Russian Federation (Grant 08-08). Issue 2 (2020) - Sanchez, Tonametl; Polyakov, Andrey; Efimov, Denis
Abstract: In this paper we propose a discretisation scheme for continuous and asymptotically stable homogeneous systems. This method is based on the dynamics of the system projected on a level surface of a homogeneous Lyapunov function. The discretisation method is explicit and preserves the convergence rate of the continuous-time system.