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Abstract <p> For single-input affine control systems, we address the problem of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10625_2025_2784_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation>-orbital feedback linearization around singularpoints of the derived flag of the distribution associated with the control system. By a singularpoint of a derived flag we mean a point such that at least one of the elements of the derived flag inany neighborhood of this point is not a distribution of constant rank. We prove a local necessaryand sufficient condition for A-orbital feedback equivalence of a single-input affine control systemto a linear controllable system considered in a neighbourhood of the zero equilibrium point.</p>

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On Singularities of \(A \)-Orbital Feedback Linearization of Single-Input Affine Controllable Systems

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • D. A. Fetisov

摘要

Abstract

For single-input affine control systems, we address the problem of \(A\) -orbital feedback linearization around singularpoints of the derived flag of the distribution associated with the control system. By a singularpoint of a derived flag we mean a point such that at least one of the elements of the derived flag inany neighborhood of this point is not a distribution of constant rank. We prove a local necessaryand sufficient condition for A-orbital feedback equivalence of a single-input affine control systemto a linear controllable system considered in a neighbourhood of the zero equilibrium point.