Absolute and input-to-state stabilities of nonautonomous systems with causal mappings

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We consider systems governed by the scalar equation Σ k=0nak(t)x(n-k)(t) = [F x](t) (t ≥ 0), where ao ≡ 1; ak(t) (k = 1,... ,n) are positive continuous functions and F is a causal mapping. We also consider the case when F depends on the input. Such equations include differential, integrodifferential and other traditional equations. It is assumed that all the roots rk(t) (k = l,...,n) of the polynomial z n + a1(t)zn-1+...+an(t) are real and negative for all t > 0. Exact explicit conditions for the absolute and input-to-state stabilities of the considered systems are established

Original languageEnglish
Pages (from-to)655-666
Number of pages12
JournalDynamic Systems and Applications
Issue number3-4
StatePublished - 1 Sep 2009


  • Absolute stability
  • Causal operators
  • Input-to-state stability
  • Nonlinear nonautonomous system

ASJC Scopus subject areas

  • General Mathematics


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