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L 2 ‐absolute and input‐to‐state stabilities of equations with nonlinear causal mappings
Author(s) -
Gil' M. I.
Publication year - 2008
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1305
Subject(s) - nonlinear system , mathematics , scalar (mathematics) , differential equation , state (computer science) , stability (learning theory) , mathematical analysis , differential (mechanical device) , physics , computer science , quantum mechanics , geometry , algorithm , machine learning , thermodynamics
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. Copyright © 2008 John Wiley & Sons, Ltd.