Stabilization of a chain of three integrators by a feedback in the form of nested saturators

Yu. V. Morozov; Морозов Ю. В.; A. V. Pesterev; Пестерев А. В.

doi:10.31857/S0002338824040121

Stabilization of a chain of three integrators by a feedback in the form of nested saturators

Authors: Morozov Y.V.¹, Pesterev A.V.¹
Affiliations:
1. V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Issue: No 4 (2024)
Pages: 167-176
Section: НАВИГАЦИОННЫЕ СИСТЕМЫ
URL: https://rjmseer.com/0002-3388/article/view/676408
DOI: https://doi.org/10.31857/S0002338824040121
EDN: https://elibrary.ru/TRFTDB
ID: 676408

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Abstract

The problem of stabilizing a chain of three integrators subject to a phase constraint by a continuous constrained control is considered. The application of a feedback in the form of nested saturators results in study of a switching system. Necessary conditions of local stability are established. A Lyapunov function is constructed by means of which it is proved that the necessary conditions are sufficient for global stability of the closed-loop system. The discussion is illustrated by numerical examples.

Keywords

stabilization of a third-order integrator, nested saturators, global asymptotic stability, Lyapunov function

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About the authors

Yu. V. Morozov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Author for correspondence.
Email: tot1983@inbox.ru
Russian Federation, Moscow

A. V. Pesterev

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Email: alexanderpesterev.ap@gmail.com
Russian Federation, Moscow

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