Investigation of the properties of the optimal set of practical semistability of solutions to systems of ordinary differential equations

Abstract

The paper investigates the properties of the optimal set of initial conditions in the problem of practical semistability of solutions to systems of ordinary differential equations. Conditions are substantiated for a point to belong to the interior and to the boundary of the optimal set. In the case of a linear homogeneous system with convex state constraints, the support function, the Minkowski functional, and the inverse Minkowski functional of the optimal semistability set are rigorously derived.