Continuous Dependence on the Impulsive Effects of Dying Solutions of Systems Differential Equations with Variable Structure and Impulses

  • Katya Dishlieva Department of Algebra and Geometry, Faculty of Applied Mathematics and Informatics, Technical University of Sofia
  • Angel Dishliev Department of Mathematics, University of Chemical Technology and Metallurgy - Sofia
  • Runyana Chukleva Department of Computer Systems and Technologies, Faculty of Electronics and Automation, Technical University of Plovdiv
  • Sashka Petkova Department of Computer Systems and Technologies, Faculty of Electronics and Automation, Technical University of Plovdiv

Abstract

Basic object of research in this paper are systems differential equations with variable structure and impulses. Switching moments, in which a change of the structure and impulsive effects on the solutions are determined by means of the switching hyperplanes, belonging to the phase space system. Changing the structure and impulsive effects on the solutions is performed at the switching moments, which are determined by the switching hyperplanes of phase space system.

The switching moments coincide with the moments, when the trajectory of corresponding initial problem meets the switching hyperplanes.

The main aim of this studies is ï¬nding the sufï¬cient conditions for continuous dependence of the solutions of systems differential equations, speciï¬ed above. We will clarify that:
- The solutions are dying due to the impulsive effects;
- Continuous dependence is on the perturbations in initial conditions and impulsive effects;
- Continuous dependence is on an arbitrary closed interval, which is contained in maximum interval of existence of the solutions.

Author Biography

Katya Dishlieva, Department of Algebra and Geometry, Faculty of Applied Mathematics and Informatics, Technical University of Sofia

Faculty of Applied Mathematics and Informatics,

Associate Professor, Ph.D.

Published
2013-04-24
How to Cite
Dishlieva, K., Dishliev, A., Chukleva, R., & Petkova, S. (2013). Continuous Dependence on the Impulsive Effects of Dying Solutions of Systems Differential Equations with Variable Structure and Impulses. European Journal of Mathematical Sciences, 2(2), 215-228. Retrieved from http://ejmathsci.org/index.php/ejmathsci/article/view/139
Section
Articles