Korobov's Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem

An extension of the solution set of the finite-time stabilization problem by bounded feedback controls, which is also called the synthesis problem for the canonical system via Korobov's nonunique controllability function, is given. We consider the case when the value of the controllability functions at the initial point is exactly the time of motion from the initial point to the origin. The family of positional controls resolving the synthesis problem is given in terms of a certain real parameter. We enlarge the interval of the parameters and explicitly compute its endpoints as functions of the dimension n of the given system.