Stability of Difference Equations and Applications to Robustness Problems

被引：0
作者：
Bogdan Sasu
机构：
[1] West University of Timişoara,Department of Mathematics, Faculty of Mathematics and Computer Science
来源：
Advances in Difference Equations | / 2010卷
关键词：
Banach Space; Difference Equation; Sequence Space; Exponential Stability; Banach Lattice;
D O I：
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摘要：
The aim of this paper is to obtain new necessary and sufficient conditions for the uniform exponential stability of variational difference equations with applications to robustness problems. We prove characterizations for exponential stability of variational difference equations using translation invariant sequence spaces and emphasize the importance of each hypothesis. We introduce a new concept of stability radius [inline-graphic not available: see fulltext][inline-graphic not available: see fulltext] for a variational system of difference equations [inline-graphic not available: see fulltext] with respect to a perturbation structure [inline-graphic not available: see fulltext] and deduce a very general estimate for the lower bound of [inline-graphic not available: see fulltext][inline-graphic not available: see fulltext]. All the results are obtained without any restriction concerning the coefficients, being applicable for any system of variational difference equations.
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