L2-instability of vector equations with nonlinear causal mappings

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Abstract

Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L 2-norm of solutions are established. The obtained estimates give us explicit conditions for the L2-stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.

Original languageEnglish
Pages (from-to)201-219
Number of pages19
JournalDynamic Systems and Applications
Volume17
Issue number1
StatePublished - 1 Mar 2008

Keywords

  • Absolute stability
  • Causal mappings
  • Difference equations with continuous time
  • Differential delay equations
  • Differential equations
  • Input-to-state stability
  • L-stability

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