ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Vibrational stabilization and Brockett problem


G. A. Leonov

Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia

M. M. Shumafov

Professor, Adyghey State University


This work is devoted to the statement of solution methods for Brokett problem - a stabilization of linear control systems with nonstationary feedback. The paper consists of two parts.

In the first part two approaches to the solving Brokett problem for continuous linear control systems are considered. One method allows obtaining a low-frequency stabilization and another - a high-frequency one. Both the methods result in obtaining necessary and sufficient conditions of stabilizability of two-dimensional ( and also three-dimensional in the first method)

The second part is devoted to the analog of Brokett problem for discrete linear control systems. The suffucient condition of low-frequency stabilization using a piecewise constant periodic function with a large enough period of feedback are given. Necessary and sufficient conditions of stabilizability of two-dimensional discrete systems are obtained.

For discrete systems with periodic feedback the problem of control of monodromic matrix spectrum is also considered.

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