Norm minimization operators for compact sets in Euclidean space

Operators formulated are projection operators generalized and minimize the Euclidean space norm functional into a non-empty intersection of a linear manifold and a ball. Equivalent canonical forms, invariants and analytic representations of minimization and acceptable solutions operators are determined. The application of operators is illustrated through an objective analysis of sufficient conditions for asymptotic stability of nonlinear differential operators of closed locally optimal automatic control systems.