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Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems

Author

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  • Robert Vrabel

    (Institute of Applied Informatics, Automation and Mechatronics, Slovak University of Technology in Bratislava, Bottova 25, 917 01 Trnava, Slovakia)

Abstract

Based on the eigenvalue idea and the time-varying weighted vector norm in the state space R n we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones.

Suggested Citation

  • Robert Vrabel, 2020. "Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems," Mathematics, MDPI, vol. 8(6), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:915-:d:367344
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