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Ellipsoidal Bounds on Reachable Sets of Dynamical Systems with Matrices Subjected to Uncertain Perturbations1

Author

Listed:
  • F. L. Chernousko

    (Russian Academy of Sciences)

  • D. Ya. Rokityanskii

    (Russian Academy of Sciences)

Abstract

Linear dynamical systems described by finite-difference or ordinary differential equations are considered. The matrix of the system is uncertain or subject to disturbances, and only the bounds on admissible perturbations of the matrix are known. Outer ellipsoidal estimates of reachable sets of the system are obtained and equations describing the evolution of the approximating ellipsoids are derived. An example is presented.

Suggested Citation

  • F. L. Chernousko & D. Ya. Rokityanskii, 2000. "Ellipsoidal Bounds on Reachable Sets of Dynamical Systems with Matrices Subjected to Uncertain Perturbations1," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 1-19, January.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:1:d:10.1023_a:1004687620019
    DOI: 10.1023/A:1004687620019
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    Cited by:

    1. C. Durieu & É. Walter & B. Polyak, 2001. "Multi-Input Multi-Output Ellipsoidal State Bounding," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 273-303, November.
    2. Steven Duda & Edeltraud Gehrig & Thomas Lorenz, 2022. "External Ellipsoidal Approximations for Set Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 759-798, March.

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