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On invariant polyhedra of continuous-time systems subject to additive disturbances. (English) Zbl 0851.93046
Summary: This paper presents new necessary and sufficient algebraic conditions on the existence of positively \({\mathcal D}\)-invariant polyhedra of continuous-time linear systems subject to additive disturbances. In particular, for a convex unbounded polyhedron containing the origin in its interior, it is also shown that the positive \({\mathcal D}\)-invariance conditions can be split into two lower-dimensional sets of algebraic relations: the first corresponds to disturbance decoupling conditions and the second to positive \({\mathcal D}\)-invariance conditions for bounded polyhedra of a reduced-order system. The stability of the overall system is discussed as well. By exploring the results obtained, a linear programming approach is proposed for solving a state-constrained regulator problem in the presence of additive disturbances.

93C73 Perturbations in control/observation systems
93D09 Robust stability
90C05 Linear programming
Full Text: DOI
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