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Stability theorems for nonlinear functional differential equations

✍ Scribed by O. Anashkin

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 783 KB
Volume: 28
Category: Article
ISSN: 0895-7177
DOI: 10.1016/s0895-7177(98)00089-2

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✦ Synopsis

new approach in stability theory for a class of retarded nonlinear functional differential equations is discussed. The problem of stability of the zero solution is considered under the assumption that the system of interest has a trivial linearization, i.e., it is essentially nonlinear. Sufficient conditions for uniform asymptotic stability and instability are given by auxiliary functionals of Lyapunov-Krasovskii type. The method is also applicable to linear systems with a small parameter in the standard form. Some examples are given.

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