L2-absolute and input-to-state stabilities of equations with nonlinear causal mappings

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8 Scopus citations


Nonlinear scalar equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norms of solutions are established. These estimates give us explicit conditions for the absolute and input-to-state stabilities of the considered equations. The Aizerman-type problem from the theory of absolute stability is also discussed. The suggested approach enables us to consider various classes of systems from the unified point of view.

Original languageEnglish
Pages (from-to)151-167
Number of pages17
JournalInternational Journal of Robust and Nonlinear Control
Issue number2
StatePublished - 25 Jan 2009


  • Absolute stability
  • Aizerman-type problem
  • Causal mappings
  • Difference equations with continuous time
  • Differential equations
  • Functional differential equations
  • Input-to-state stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Chemical Engineering (all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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