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Lyapunov‐based consistent discretization of stable homogeneous systems
Author(s) -
Sanchez Tonametl,
Polyakov Andrey,
Efimov Denis
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5308
Subject(s) - discretization , lyapunov function , homogeneous , mathematics , convergence (economics) , lyapunov redesign , stability theory , lyapunov equation , control theory (sociology) , stability (learning theory) , exponential stability , scheme (mathematics) , function (biology) , computer science , mathematical analysis , nonlinear system , control (management) , physics , quantum mechanics , combinatorics , artificial intelligence , machine learning , evolutionary biology , economics , biology , economic growth
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.