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Invariants of Linear Control Systems with Analytic Matrices and the Linearizability Problem

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Abstract

The paper continues the authors’ study of the linearizability problem for nonlinear control systems. In the recent work (Sklyar, Syst Control Lett 134:104572, 2019), conditions on mappability of a nonlinear control system to a preassigned linear system with analytic matrices were obtained. In the present paper, we solve more general problem on linearizability conditions without indicating a target linear system. To this end, we give a description of invariants for linear nonautonomous single-input controllable systems with analytic matrices, which allow classifying such systems up to transformations of coordinates. This study leads to one problem from the theory of linear ordinary differential equations with meromorphic coefficients. As a result, we obtain a criterion for mappability of nonlinear control systems to linear control systems with analytic matrices.

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Acknowledgements

The authors are sincerely grateful to the anonymous reviewers for their detailed comments and constructive suggestions.

Funding

This work was financially supported by Polish National Science Centre grant no. 2017/25/B/ST1/ 01892.

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Authors and Affiliations

  1. Institute of Mathematics, University of Szczecin, Wielkopolska str. 15, Szczecin, 70-451, Poland

    K. V. Sklyar

  2. V. N. Karazin Kharkiv National University, Svobody sqr. 4, Kharkiv, 61022, Ukraine

    S. Yu. Ignatovich

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  1. K. V. Sklyar
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  2. S. Yu. Ignatovich
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Correspondence to S. Yu. Ignatovich.

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Sklyar, K.V., Ignatovich, S.Y. Invariants of Linear Control Systems with Analytic Matrices and the Linearizability Problem. J Dyn Control Syst 29, 111–128 (2023). https://doi.org/10.1007/s10883-021-09574-x

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  • DOI: https://doi.org/10.1007/s10883-021-09574-x

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