On Convergence of External Ellipsoidal Approximations of the Reachability Domains of Discrete Dynamic Linear Systems

  • Authors:

  • A. V. Nazin;S. A. Nazin;B. T. Polyak

  • Affiliations:

  • Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia;Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia;Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2004

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Abstract

The ellipsoid technique is widely used in the guaranteed estimation for approximation of the reachability domains of dynamic systems. The present paper considered the issues of external ellipsoidal estimation of the current and limiting reachability sets of a stable discrete dynamic linear system. Recurrent estimation algorithms using the criterion of minimum trace of the “weighted” ellipsoid matrix were developed for these systems, and their limiting properties were considered.