Some Economic Dynamics Problems for Hybrid Models with Aftereffect

Abstract

In this paper, we consider a class of economic dynamics models in the form of linear functional differential systems with continuous and discrete times (hybrid models) that covers many kinds of dynamic models with aftereffect. The focus of attention is periodic boundary value problems with deviating argument, control problems with respect to general on-target vector-functional and questions of stability to solutions. For boundary value problems, some sharp sufficient conditions of the unique solvability are obtained. The attainability of on-target values is under study as applied to control problems with polyhedral constraints with respect to control, some estimates of the attainability set as well as estimates to a number of switch-points of programming control are presented. For a class of hybrid systems, a description of asymptotic properties of solutions is given.