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Stability and linearization: discrete-time systems

✍ Scribed by Irwin W. Sandberg

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
83 KB
Volume
30
Category
Article
ISSN
0098-9886

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✦ Synopsis

Abstract

A theorem by Hadamard gives a two‐part condition under which a map from one Banach space to another is a homeomorphism. The theorem, while often very useful, is incomplete in the sense that it does not explicitly specify the family of maps for which the condition is met. Recently, under a typically weak additional assumption on the map, it was shown that Hadamard's condition is met if and only if the map is a homeomorphism with a Lipschitz continuous inverse. Here an application is given concerning the relation between the stability of a discrete‐time non‐linear system and the stability of related linear systems. Copyright Β© 2002 John Wiley & Sons, Ltd.

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