On the exponential stability of dynamic equations on time scales (Q878484)
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scientific article; zbMATH DE number 5146732
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the exponential stability of dynamic equations on time scales |
scientific article; zbMATH DE number 5146732 |
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On the exponential stability of dynamic equations on time scales (English)
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26 April 2007
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The authors prove various results on exponential stability of linear and nonlinear dynamic equations \( x^\Delta (t) = F(t,x) \) on a time scale \(\mathbb{T}\) ( = arbitrary closed subset of the reals). There are theorems on linearized stability, Perron's Theorem about input-output stability, a characterization of uniform exponential stability of linear equations. Since the paper deals with bounded below time scales the usual condition of regressivity of the equation can be dropped.
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Perron's theorem
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