Simple and weak Δ-invariant polyhedral sets for discrete-time singular systems

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 Δ-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak Δ-invariance are considered. They can be seen as extensions of the Δ-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.