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Simple and weak D-invariant psolyhedral sets for discrete-time singular systems

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Author(s): Castelan Eugênio B. | Tarbouriech Sophie

Journal: Sba: Controle & Automação Sociedade Brasileira de Automatica
ISSN 0103-1759

Volume: 14;
Issue: 4;
Start page: 339;
Date: 2003;
Original page

Keywords: Singular systems | Disturbances | Convex polyhedra | Invariance | Initial conditions

ABSTRACT
In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of delta-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak delta-invariance are considered. They can be seen as extensions of the delta-positive invariance concept used for the regular linear systems with additive disturbances. The results are presented by considering classical equivalent system representations for linear singular systems.
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