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

Efimov, Denis; Polyakov, Andrey; Aleksandrov, Alexander

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1016/j.automatica.2019.108546

Title :

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

Author(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]

Journal title :

Automatica

Publisher :

Elsevier

Publication date :

2019

ISSN :

0005-1098

English keyword(s) :

Discretization
Homogeneous systems
Euler method

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

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

Collections :