Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can b...

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Detalles Bibliográficos
Autores: De la Sen Parte, Manuel, Ibeas Hernández, Asier
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/15738
Acceso en línea:http://hdl.handle.net/10810/15738
Access Level:acceso abierto
Palabra clave:discrete-continuous systems
time-invariant systems
proximity points
differential-equations
adaptive-control
cyclic mappings
metric-spaces
stability
delays
positivity
expansive
non-expansive
contractive and strictly contractive self-mappings
switched dynamic systems
convergence
fixed point
ANALYSIS
DISCRETE MATHEMATICS AND COMBINATORICS
MATHEMATICS, APPLIED
Descripción
Sumario:This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.