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(A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems

Author

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  • C. E. T. Dórea

    (Universidade Federal de Bahia, Salvador)

  • J. C. Hennet

    (Centre National de la Recherche Scientifique)

Abstract

The problem of confining the trajectory of a linear discrete-time system in a given polyhedral domain is addressed through the concept of (A, B)-invariance. First, an explicit characterization of (A, B)-invariance of convex polyhedra is proposed. Such characterization amounts to necessary and sufficient conditions in the form of linear matrix relations and presents two major advantages compared to the ones found in the literature: it applies to any convex polyhedron and does not require the computation of vertices. Such advantages are felt particularly in the computation of the supremal (A, B)-invariant set included in a given polyhedron, for which a numerical method is proposed. The problem of computing a control law which forces the system trajectories to evolve inside an (A, B)-invariant polyhedron is treated as well. Finally, the (A, B)-invariance relations are generalized to persistently disturbed systems.

Suggested Citation

  • C. E. T. Dórea & J. C. Hennet, 1999. "(A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 521-542, December.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:3:d:10.1023_a:1021727806358
    DOI: 10.1023/A:1021727806358
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    Cited by:

    1. Andreas Ernst & Lars Grüne & Janosch Rieger, 2023. "A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems," Journal of Global Optimization, Springer, vol. 86(2), pages 521-543, June.

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