On the External Estimation of the Limit Reachable Set for the Linear Discrete-Time System Based on Support Hyperplanes

Abstract

A linear discrete-time system with geometric constraints on control is considered. For the given system, the problem of constructing the limit reachable set is solved. It is proven that it is a cylinder oriented along certain elements of the real Jordan basis. Statements about the structure of the supporting hyperplane to the convex section of this cylinder are formulated and proven. Necessary and sufficient conditions for the boundedness of the limit reachable set are determined.