Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step

Efimov, Denis; Polyakov, Andrey; Aleksandrov, Alexander

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1016/j.automatica.2019.108546

Titre :

Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step

Auteur(s) :

Efimov, Denis [Auteur]

Finite-time control and estimation for distributed systems [VALSE]
Polyakov, Andrey [Auteur]

Finite-time control and estimation for distributed systems [VALSE]
Aleksandrov, Alexander [Auteur]
Saint Petersburg University [SPBU]

Titre de la revue :

Automatica

Éditeur :

Elsevier

Date de publication :

2019

ISSN :

0005-1098

Mot(s)-clé(s) en anglais :

Discretization
Homogeneous systems
Euler method

Discipline(s) HAL :

Sciences de l'ingénieur [physics]/Automatique / Robotique

Résumé en anglais : [en]

Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration ...
Lire la suite >Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Différentiateurs et commandes homogènes par modes glissants multivalués en temps discret: l'approche implicite

Collections :