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

Abstract

We investigate properties of the optimal set of initial conditions in the problem of practical semistability of solutions of systems of ordinary differential equations. We establish conditions of belonging of a point to the interior and the boundary of this set. In the case of a linear homogeneous system with convex state constraints, we substantiate the convexity of the optimal set of practical semistability and obtain its support function, the Minkowski function, and the inverse Minkowski function.