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Asymptotic Behavior of the Attainable Sets of Linear Periodic Control Systems

Author

Listed:
  • T. Yu. Figurina

    (Russian Academy of Sciences)

  • A. I. Ovseevich

    (Russian Academy of Sciences)

Abstract

This paper deals with the attainable sets of linear periodic control systems. The asymptotic behavior of the attainable sets over a long time interval is investigated in terms of shapes of the sets. The shape of a set stands for the totality of all its images under nonsingular linear transformations. It is shown that there exist limits of the shape of attainable sets corresponding to time instants with the same residue modulo the period of the system and that the limit shapes are different if the system includes a stable subsystem.

Suggested Citation

  • T. Yu. Figurina & A. I. Ovseevich, 1999. "Asymptotic Behavior of the Attainable Sets of Linear Periodic Control Systems," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 349-364, February.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:2:d:10.1023_a:1021734319813
    DOI: 10.1023/A:1021734319813
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    Cited by:

    1. Elena Goncharova & Alexander Ovseevich, 2013. "Limit Behavior of Reachable Sets of Linear Time-Invariant Systems with Integral Bounds on Control," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 400-415, May.
    2. H. W. Lou, 2004. "On the Attainable Sets of Control Systems with p-Integrable Controls," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 123-147, October.

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