On invariant polyhedra of continuous-time systems subject to additive disturbances.

*(English)*Zbl 0851.93046Summary: 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.

##### MSC:

93C73 | Perturbations in control/observation systems |

93D09 | Robust stability |

90C05 | Linear programming |

##### Keywords:

positively \({\mathcal D}\)-invariant polyhedra; additive disturbances; disturbance decoupling conditions; stability; linear programming
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\textit{B. E. A. Milani} and \textit{C. E. T. Dórea}, Automatica 32, No. 5, 785--789 (1996; Zbl 0851.93046)

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