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

Proof of the Stabilization Theorem for a Linear Dynamic System of Unknown Order with Variable Parameters

Author(s):

Boris Vasilievich Ulanov

Togliatti State University,
Dotsent of the Department of Higher Mathematics and Mathematical Education,
Togliatti, Belorusskaya Street, 14
Candidate of physical and mathematical sciences, dotsent

bv_ulanov@mail.ru

Abstract:

The proof of the stabilization theorem for a linear dynamic system described by one differential equation of unknown order which does not exceed a given natural number, and with parameters that vary within any given limits is presented. For the synthesis of the control, it is necessary to know the limits within which the parameters of the differential equation and all derivatives of these parameters (up to the order less by one than a given natural number) are changed.

Keywords

• dynamic system
• order of a differential equation
• parameters of a linear differential equation
• stabilization

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