Integrally small perturbations of linear nonautonomous systems

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Abstract

Let A(t) and B(t) (t ≥ 0) be variable n × n-matrices. Assuming that the system ẋ = A(t)x is exponentially stable and the matrix norm of the integral ∫ t 0 (B(s) - A(s)) ds is sufficiently small, for the system ẋ = B(t)x we derive explicit stability conditions, which improve the well-known ones in appropriate situations. The results are illustrated by a numerical example.

Original languageEnglish
Pages (from-to)361-369
Number of pages9
JournalCircuits, Systems, and Signal Processing
Volume31
Issue number1
DOIs
StatePublished - 1 Feb 2012

Keywords

  • Linear nonautonomous systems
  • Stability

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