document: L/sub p / stability and linearization 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 L/sub p / stability -LRB- with 1 < or = p < infinity -RRB- of a nonlinear system and the stability of related linear systems . We also give a result that directs attention to a fundamental limitation concerning what can be proved about linearization and stability for a related familiar family of feedback systems
doc_bio_tags: O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I
extractive_keyphrases: banach space lipschitz continuous inverse nonlinear system linear systems feedback systems
abstractive_keyphrases: hadamard's condition l/sub p/ stability