About the method for constructing external estimates of the limit controllability set for the linear discrete-time system with bounded control

This article discusses the problem of constructing an external estimate of the limit set of controllability for a linear discrete system with convex control constraints. We have proposed a decomposition method that allows us to reduce the problem for the initial system to subsystems of smaller dimension by switching to the normal Jordan basis of the matrix of the system. The statement about the structure of the reference hyperplane to the limit set of controllability is formulated and proved. A method for constructing an external estimate of the limit set of controllability with an arbitrary order of accuracy in the sense of the Hausdorff distance is proposed based on the principle of contraction mappings. The paper provides examples.