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Estimation of the Attraction Domain for an Affine System with Constrained Vector Control Closed by the Linearizing Feedback

  • Nonlinear Systems
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Abstract

Nonlinear affine systems with constrained vector control that are represented in a canonical (normal) form and are closed by feedbacks linearizing the system in a neighborhood of the origin, are considered. For the nonlinear closed-loop system, the problem is set to construct an estimate of the attraction domain of an equilibrium position. A method for constructing an estimate of the attraction domain, which is based on results of absolute stability theory, is suggested. The estimate is sought as a Cartesian product of positive invariant sets of the subsystems composing the system. In the case of ellipsoidal invariant sets, construction of the estimate reduces to solving a system of linear matrix inequalities. The discussion is illustrated by numerical examples.

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Authors and Affiliations

  1. Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. V. Pesterev

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  1. A. V. Pesterev
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Correspondence to A. V. Pesterev.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 5, pp. 66–85.

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Pesterev, A.V. Estimation of the Attraction Domain for an Affine System with Constrained Vector Control Closed by the Linearizing Feedback. Autom Remote Control 80, 840–855 (2019). https://doi.org/10.1134/S0005117919050047

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  • DOI: https://doi.org/10.1134/S0005117919050047

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