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

On the stability of solutions of certain linear set differential equations