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Avtomat. i Telemekh., 2019, Issue 5, Pages 66–85 (Mi at15112)  

Nonlinear Systems

Estimation of the attraction domain for an affine system with constrained vector control closed by the linearizing feedback

A. V. Pesterev

Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: Nonlinear affine systems with constrained vector control that are represented in a canonical (normal) form and are closed by feedbacks linearizing the system in a neighborhood of the origin, are considered. For the nonlinear closed-loop system, the problem is set to construct an estimate of the attraction domain of an equilibrium position. A method for constructing an estimate of the attraction domain, which is based on results of absolute stability theory, is suggested. The estimate is sought as a Cartesian product of positive invariant sets of the subsystems composing the system. In the case of ellipsoidal invariant sets, construction of the estimate reduces to solving a system of linear matrix inequalities. The discussion is illustrated by numerical examples.

Keywords: nonlinear affine systems with constrained control, attraction domain, absolute stability theory, linear matrix inequalities (LMIs).

Funding Agency Grant Number
Russian Foundation for Basic Research 18-08-00531_ŕ
Russian Academy of Sciences - Federal Agency for Scientific Organizations 29
This work was supported by the Russian Foundation for Basic Research, project no. 18-08-00531, and by the Presidium of Russian Academy of Sciences, Program no. 29 “Advanced Topics of Robotic Systems.”


DOI: https://doi.org/10.1134/S0005231019050040

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English version:
Automation and Remote Control, 2019, 80:5, 840–855

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: A. P. Krishchenko

Received: 25.07.2018
Revised: 25.07.2018
Accepted: 08.11.2018

Citation: A. V. Pesterev, “Estimation of the attraction domain for an affine system with constrained vector control closed by the linearizing feedback”, Avtomat. i Telemekh., 2019, no. 5, 66–85; Autom. Remote Control, 80:5 (2019), 840–855

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