Teixeira singularities in 3D switched feedback control systems

A Colombo; M di Bernardo; E Fossas; Mike R Jeffrey

doi:10.1016/j.sysconle.2010.07.006

Teixeira singularities in 3D switched feedback control systems

A Colombo, M di Bernardo, E Fossas, Mike R Jeffrey

Department of Mathematical Sciences

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Abstract

This paper is concerned with the analysis of a singularity that can occur in three-dimensional discontinuous feedback control systems. The singularity is the two-fold — a tangency of orbits to both sides of a switching manifold. Particular attention is placed on the Teixeira singularity, which previous literature suggests as a mechanism for dynamical transitions in this class of systems. We show that such a singularity cannot occur in classical single-input single-output systems in the Lur’e form. It is, however, a potentially dangerous phenomenon in multiple-input multiple-output switched control systems. The theoretical derivation is illustrated by means of a representative example.

Original language	English
Pages (from-to)	615-622
Number of pages	8
Journal	Systems & Control Letters
Volume	59
Issue number	10
DOIs	https://doi.org/10.1016/j.sysconle.2010.07.006
Publication status	Published - 2010

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10.1016/j.sysconle.2010.07.006

2009SCL_LureTeixeira~.pdf
NOTICE: this is the author’s version of a work that was accepted for publication in Systems & Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Colombo, A., di Bernardo, M., Fossas, E. and Jeffrey, M. R., 2010. Teixeira singularities in 3D switched feedback control systems. Systems & Control Letters, 59 (10), pp. 615-622. DOI:http://dx.doi.org/10.1016/j.sysconle.2010.07.006
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AU - Fossas, E

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N2 - This paper is concerned with the analysis of a singularity that can occur in three-dimensional discontinuous feedback control systems. The singularity is the two-fold — a tangency of orbits to both sides of a switching manifold. Particular attention is placed on the Teixeira singularity, which previous literature suggests as a mechanism for dynamical transitions in this class of systems. We show that such a singularity cannot occur in classical single-input single-output systems in the Lur’e form. It is, however, a potentially dangerous phenomenon in multiple-input multiple-output switched control systems. The theoretical derivation is illustrated by means of a representative example.

AB - This paper is concerned with the analysis of a singularity that can occur in three-dimensional discontinuous feedback control systems. The singularity is the two-fold — a tangency of orbits to both sides of a switching manifold. Particular attention is placed on the Teixeira singularity, which previous literature suggests as a mechanism for dynamical transitions in this class of systems. We show that such a singularity cannot occur in classical single-input single-output systems in the Lur’e form. It is, however, a potentially dangerous phenomenon in multiple-input multiple-output switched control systems. The theoretical derivation is illustrated by means of a representative example.

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Teixeira singularities in 3D switched feedback control systems

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