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Causality and stability conditions for the control of a linear distributed system

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Abstract

For a linear distributed system controlled by nonlinear feedback, a sufficient condition for the existence, causality, and boundedness of an operator that transforms the external action and initial state of the system to the behavior of the output of a closed-loop system is formulated. A procedure is designed for determining the class of feedbacks ensuring the causality and stability of the closed-loop control system. It is applicable to a linear one-dimensional heat conduction system controlled by nonlinear temperature feedback to the boundary action.

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Authors and Affiliations

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

    E. M. Solnechnyi

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  1. E. M. Solnechnyi
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Original Russian Text © E.M. Solnechnyi, 2006, published in Avtomatika i Telemekhanika, 2006, No. 4, pp. 53–85.

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Solnechnyi, E.M. Causality and stability conditions for the control of a linear distributed system. Autom Remote Control 67, 562–588 (2006). https://doi.org/10.1134/S0005117906040059

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  • DOI: https://doi.org/10.1134/S0005117906040059

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