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On the Output Stabilization Problem: Constructing a Delay Feedback for a Chain of Integrators

  • LINEAR SYSTEMS
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Abstract

A feedback structure stabilizing an \( n \)-fold integrator with even \( n \) is proposed. It is well known that for many differential systems, in particular, for models of mechanical systems, stabilization problems can be transformed into a special form containing a chain of integrators as a subsystem. The control constructed for an arbitrary even order of the integrator is a linear combination of coordinates of the delay state with odd indices and depends on three numerical parameters. These parameters satisfy constraints of a simple form and can vary widely depending on the control performance requirements. Examples of more general system structures are given for which the control constructed ensures the asymptotic stability of the equilibrium. The stability properties of cascade delay systems are used to prove the stabilizing properties of the control.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    O. V. Druzhinina

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    O. V. Druzhinina

  3. Ulyanovsk State University, Ulyanovsk, 432970, Russia

    N. O. Sedova

Authors
  1. O. V. Druzhinina
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  2. N. O. Sedova
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Correspondence to O. V. Druzhinina or N. O. Sedova.

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Translated by V. Potapchouck

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Druzhinina, O.V., Sedova, N.O. On the Output Stabilization Problem: Constructing a Delay Feedback for a Chain of Integrators. Autom Remote Control 83, 180–190 (2022). https://doi.org/10.1134/S0005117922020023

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  • DOI: https://doi.org/10.1134/S0005117922020023

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