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Stabilization of linear autonomous systems of differential equations with distributed delay

  • Stability of Systems
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Abstract

Consideration is given to the problem of optimal stabilization of differential equation systems with distributed delay. The optimal stabilizing control is formed according to the principle of feedback. The formulation of the problem in the functional space of states is used. It was shown that coefficients of the optimal stabilizing control are defined by algebraic and functional-differential Riccati equations. To find solutions to Riccati equations, the method of successive approximations is used. The problem for this control law and performance criterion is to find coefficients of a differential equation system with distributed delay, for which the chosen control is a control of optimal stabilization. A class of control laws for which the posed problem admits an analytic solution is described.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    Yu. F. Dolgii

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Original Russian Text © Yu.F. Dolgii, 2007, published in Avtomatika i Telemekhanika, 2007, No. 10, pp. 92–105.

This work was supported by the Basic Research Program “Control Processes” of the Presidium of the Russian Academy of Sciences and Russian Foundation for Basic Research, project no. 06-01-00399.

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Dolgii, Y.F. Stabilization of linear autonomous systems of differential equations with distributed delay. Autom Remote Control 68, 1813–1825 (2007). https://doi.org/10.1134/S0005117907100098

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  • DOI: https://doi.org/10.1134/S0005117907100098

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