IJPAM: Volume 72, No. 3 (2011)

MODELING USING DIFFERENTIAL EQUATIONS
WITH VARIABLE STRUCTURE AND IMPULSES

R.B. Chukleva
Department of Computer Systems and Technologies
Technical University Sofia, Branch Plovdiv
25, Tzanko Dyustabanov Str., Plovdiv, 4000, BULGARIA


Abstract. The modeling of shutter dynamics of a blow back valve is described with the systems of differential equations with variable structure and impulses in the present paper. The changes of the right-hand side of the system and impulsive perturbations take place at the moments when the so called ``shifting functions'' cancel (become zero). The structure of the modeling system changes depending on the states ``closed'' and ``open'' of the shutter valve. The impulses reflect the instantaneous change of the shutter valve speed during the switching from open to close position and intermittent shifting of the shutter valve. The main result in this paper is finding the suitable conditions which ensure the continuous dependence of the modeling system regarding the changes of the initial condition and switching functions.

Received: May 2, 2011

AMS Subject Classification: 34A37, 70K20

Key Words and Phrases: variable structure, variable impulsive moments, switching functions, continuous dependence, valve

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 3