PROPERTIES OF THE SET OF SOLUTIONS AND AN ENSEMBLE OF TRAJECTORIES OF A DIFFERENTIAL INCLUSION WITH A DELAY ARGUMENT

Otakulov Salim; Kholiyarova Feruza Khafizovna

doi:10.5281/zenodo.7655375

PROPERTIES OF THE SET OF SOLUTIONS AND AN ENSEMBLE OF TRAJECTORIES OF A DIFFERENTIAL INCLUSION WITH A DELAY ARGUMENT

20.02.2023 International Scientific Journal "Science and Innovation". Series A. Volume 2 Issue 2

Otakulov Salim, Kholiyarova Feruza Khafizovna

Abstract. In this paper, a mathematical model of the control object in the form of a differential inclusion with a delay argument. For such models of dynamical systems, the Cauchy problem is studied. Some properties of the set of solutions and the ensemble of trajectories of the considered class of differential inclusions are studied. Conditions for continuous dependence, closedness, and convexity of multivalued mappings related to the studied properties of differential inclusions are obtained.

Keywords: differential inclusion, delay argument, Cauchy problem, sets of solutions, ensemble of trajectories, continuous dependence, closedness, convexity.

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