Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states

For linear discrete time dynamical systems, necessary and sufficient conditions are given for a control sequence, belonging to a polyhedral constraint set, to stabilize the system under the condition that the state is restricted to a polyhedral state constraint set. A variable structure linear state feedback controller, given in terms of the controls at the vertices of the polyhedral state constraint set, is presented.