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Abstract <p> The problem of stabilizing the origin is solved for dynamical systems written in a formthat admits state feedback linearization, taking into account the magnitude constraints on thestate variable values. Based on known results on the possibility of obtaining identical control lawswhen using the integrator backstepping and the state feedback linearization methods to designstabilizing feedbacks, sufficient conditions are proposed for the gain coefficients and roots of thecharacteristic polynomial of the closed-loop system that ensure the validity of the specifiedconstraints. The resulting conditions guaranteeing that the constraints hold are based on theresults obtained using the integrator backstepping method combined with logarithmic barrierLyapunov functions. As an example, a solution of the problem of controlling a generalizedcoordinate is considered for a mechanical system whose dynamics with respect to the selectedgeneralized variable can be represented as a chain of fourth-order integrators, taking into accountthe constraints on the values of the generalized coordinate, velocity, acceleration, and jerk.</p>

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Stabilization of State Feedback Linearizable Dynamical Systems under State Constraints

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • A. E. Golubev

摘要

Abstract

The problem of stabilizing the origin is solved for dynamical systems written in a formthat admits state feedback linearization, taking into account the magnitude constraints on thestate variable values. Based on known results on the possibility of obtaining identical control lawswhen using the integrator backstepping and the state feedback linearization methods to designstabilizing feedbacks, sufficient conditions are proposed for the gain coefficients and roots of thecharacteristic polynomial of the closed-loop system that ensure the validity of the specifiedconstraints. The resulting conditions guaranteeing that the constraints hold are based on theresults obtained using the integrator backstepping method combined with logarithmic barrierLyapunov functions. As an example, a solution of the problem of controlling a generalizedcoordinate is considered for a mechanical system whose dynamics with respect to the selectedgeneralized variable can be represented as a chain of fourth-order integrators, taking into accountthe constraints on the values of the generalized coordinate, velocity, acceleration, and jerk.