Оцінка області стійкості параметричних систем за наявності крайових умов інтегральної форми

Л. А. Панталієнко


UDC 681.5.07




L. A. Pantaliyenko


         Article dynamics of the system to consider a finite period of time, and the initial phase conditions and restrictions set in concrete form. These features relate to practical stability problems associated with the design of complex systems, their management, adaptation and sensitivity.

Unlike classical methods, analysis of parametric systems from the point of practical stability can significantly expand the range of studied problems and solve them numerically. In particular, when designing circulated real systems problem of sensitivity (calculation parameters tolerances, limited and guaranteed sensitivity)

covered by the productions of the practical stability of the parametric systems in relevant space of functions.

The work, based on practical stability methods, investigated parametric system of ordinary differential equations in the presence of boundary conditions.

Topicality. The need to consider problems related to stability analysis determined high demands on system design and is directly related to its capacity for work in real conditions, particularly in boundary value problems, optimization problems of linear resonance accelerators. Focuses on practical methods of resistance with algorithmic orientation. The focus is on practical methods of stability with algorithmic orientation.

         The aim of research ─ development of numerical methods for solving problems of practical parametric stability for systems of differential equations in the presence of boundary conditions.

Materials and methods of research. The paper used methods of stability theory, differential equations and algorithms optimization.

Results. For parametric linear systems of differential equations at presence disturbances and boundary conditions forms an integrated numerical calculation carried out in the field of stability defined structures.


Formulated objectives of practical stability of parametric systems of ordinary differential equations in the presence of boundary conditions. For linear inhomogeneous systems with boundary conditions forms an integral received optimal evaluation of areas initial conditions defined structures.


Повний текст:



Bublyk, B. N., Harashchenko, F. H., Kyrychenko, N. F. (1985). Strukturno-parametrycheskaia optymyzatsyia y ustoichyvost dynamyky puchkov [Structural-parametric optimization and stability of beam dynamics]. Kyiv, Ukraine: Scientific thought, 304.

Harashchenko, F. H., Pantalienko, L. A. (1995). Analiz ta otsinka parametrychnykh system: Navch. posibnyk [Analysis and evaluation of parametric systems: Teach. Manual]. Kyiv, Ukraine: , 140. / F.H. Harashchenko, L.A. Pantalienko. – K.:ISSE, 1995. – 140 s.

Pantaliienko, L. A. (2010). Rozrakhunok oblastei parametrychnoi stiikosti za naiavnosti postiino diiuchykh zburen [The calculation of areas parametric stability at presence permanent perturbations]. Scientific Journal NUBaN Ukraine. A series of «Technology and Energy AIC», 150, 126−131.

Rozenvasser, E. N., Yusupov, R. M. (1981). Chuvstvytelnost system upravlenyia [Sensitivity control systems]. Moscow, Russia: Science, 464.

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