An exact analytical description of reachablity set for asymptotically stable linear discrete systems with constrained l1-norm scalar control

Аuthors

Sirotin A. N.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: asirotin2@mail.ru

Abstract

A linear stationary system with discrete time and scalar control is considered. It is assumed that the control is restricted on -norm, i.e. the sum of modules of control actions on each pitch is restricted and the Kalman rank condition is satisfied. A construction problem is investigated in regard to the reachability set for such class of systems. The investigation is carried out for systems with spectral matrix radius less than unity. It is shown for this case commonly encountered in practice that the required set admits exact analytical description. The set represents some convex restricted closed polyhedron with a finite number of vertices. An estimate is obtained for the number of polyhedron vertices.