In this paper we study the geometrical properties of the set of reachable states of a single input discrete-time linear time invariant (LTI) system with positive controls. This set is a cone and it can be expressed as the direct sum of a linear subspace arid a proper cone. In order to give a complete geometrical characterization of the reachable set, we provide a formula to evaluate the dimension of the largest reachable subspace and necessary and sufficient conditions for polyhedrality of the proper cone in terms of eigenvalues location. © 2006 Society for Industrial and Applied Mathematics.
The geometry of the reachability set for linear discrete-time systems with positive controls / Benvenuti, Luca; Farina, Lorenzo. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - 28:2(2006), pp. 306-325. (Intervento presentato al convegno 16th International Symposium on the Mathematical Theory of Networks and Systems tenutosi a Leuven, Belgium nel 2004) [10.1137/040612531].
The geometry of the reachability set for linear discrete-time systems with positive controls
BENVENUTI, Luca;FARINA, Lorenzo
2006
Abstract
In this paper we study the geometrical properties of the set of reachable states of a single input discrete-time linear time invariant (LTI) system with positive controls. This set is a cone and it can be expressed as the direct sum of a linear subspace arid a proper cone. In order to give a complete geometrical characterization of the reachable set, we provide a formula to evaluate the dimension of the largest reachable subspace and necessary and sufficient conditions for polyhedrality of the proper cone in terms of eigenvalues location. © 2006 Society for Industrial and Applied Mathematics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
