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

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

Stabilization Problem Solution for One Class of Nonlinear Systems with a Lagging Argument

Author(s):

I. E. Zuber

Saint-Petersburg State University
Russia, 198904, Saint-Petersburg, Petrodvoretz, Bibliotechnaya pl., 2

zuber@EZ7332.spb.edu

Abstract:

A class of multivariable nonlinear systems with a lagging argument is considered. Such a systems often encounter when models of bialogical or physical processes are constructed. Two solutions of stabilization problem are received. The first solution is based on the nonlinear stability transformation with lagging argument which provides the Frobenious form for matrix of closed loop transformed system. The second solution of stabilization problem is based on nonlinear stability transformation with lagging argument which provides the Frobenious form with the last functional column only for the object matrix of transformed system and the form of the first unit orth for vector of control distribution of transformed system. The existence conditions and explicit form of both similarity transformation are formed. The solution of stabilization problem based on both similarity transformation is received in explicit form.

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