This article is cited in 14 papers

Stability of Systems

Stabilization of linear autonomous systems of differential equations with distributed delay

Yu. F. Dolgii

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

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.

PACS: 02.30.Oz

Presented by the member of Editorial Board: A. I. Kibzun

Received: 14.12.2006

 English version: Automation and Remote Control, 2007, 68:10, 1813–1825

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