On the stability of solutions of certain linear set differential equations

Abstract

New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable operator was proved. We consider the orbit of the action of homotheties group on the space of nonempty convex compacts ($\conv\Bbb R^n$) as the form of a convex compact. For equations with periodic operator in the two-dimensional space the asymptotic stability conditions were established.