ISS implies iISS even for switched and time-varying systems (if you are careful enough)

"For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictly stronger than integral-ISS (iISS). Known proofs of the fact that ISS implies iISS employ Lyapunov characterizations of both properties. For time-varying and switched systems, such Lyapunov charac...

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Autores principales: Haimovich, Hernán, Mancilla-Aguilar, J. L.
Formato: Artículos de Publicaciones Periódicas acceptedVersion
Lenguaje:Inglés
Publicado: 2020
Materias:
SISTEMAS NO LINEALES
SISTEMAS TIEMPO VARIANTES
FUNCIONES DE LYAPUNOV
INVARIANCIA
SISTEMAS DE CONMUTACION
Acceso en línea:http://ri.itba.edu.ar/handle/123456789/1859
Aporte de:
Repositorio Institucional Instituto Tecnológico de Buenos Aires (ITBA) de Instituto Tecnológico de Buenos Aires (ITBA)
id I32-R138-123456789-1859
record_format dspace
spelling I32-R138-123456789-18592022-12-07T13:06:01Z ISS implies iISS even for switched and time-varying systems (if you are careful enough) Haimovich, Hernán Mancilla-Aguilar, J. L. SISTEMAS NO LINEALES SISTEMAS TIEMPO VARIANTES FUNCIONES DE LYAPUNOV INVARIANCIA SISTEMAS DE CONMUTACION "For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictly stronger than integral-ISS (iISS). Known proofs of the fact that ISS implies iISS employ Lyapunov characterizations of both properties. For time-varying and switched systems, such Lyapunov characterizations may not exist, and hence establishing the exact relationship between ISS and iISS remained an open problem, until now. In this paper, we solve this problem by providing a direct proof, i.e. without requiring Lyapunov characterizations, of the fact that ISS implies iISS, in a very general time-varying and switched-system context. In addition, we show how to construct suitable iISS gains based on the comparison functions that characterize the ISS property, and on bounds on the function f defining the system dynamics. When particularized to time-invariant systems, our assumptions are even weaker than existing ones. Another contribution is to show that for time-varying systems, local Lipschitz continuity of f in all variables is not sufficient to guarantee that ISS implies iISS. We illustrate application of our results on an example that does not admit an iISS-Lyapunov function." 2020-01-14T13:20:13Z 2020-01-14T13:20:13Z 2019-06 Artículos de Publicaciones Periódicas info:eu-repo/semantics/acceptedVersion 0005-1098 http://ri.itba.edu.ar/handle/123456789/1859 en info:eu-repo/semantics/altIdentifier/doi/10.1016/j.automatica.2019.02.057 info:eu-repo/grantAgreement/ANPCyT/PICT/2014-2599/AR. Ciudad de Buenos Aires. application/pdf
institution Instituto Tecnológico de Buenos Aires (ITBA)
institution_str I-32
repository_str R-138
collection Repositorio Institucional Instituto Tecnológico de Buenos Aires (ITBA)
language Inglés
topic SISTEMAS NO LINEALES
SISTEMAS TIEMPO VARIANTES
FUNCIONES DE LYAPUNOV
INVARIANCIA
SISTEMAS DE CONMUTACION
spellingShingle SISTEMAS NO LINEALES
SISTEMAS TIEMPO VARIANTES
FUNCIONES DE LYAPUNOV
INVARIANCIA
SISTEMAS DE CONMUTACION
Haimovich, Hernán
Mancilla-Aguilar, J. L.
ISS implies iISS even for switched and time-varying systems (if you are careful enough)
topic_facet SISTEMAS NO LINEALES
SISTEMAS TIEMPO VARIANTES
FUNCIONES DE LYAPUNOV
INVARIANCIA
SISTEMAS DE CONMUTACION
description "For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictly stronger than integral-ISS (iISS). Known proofs of the fact that ISS implies iISS employ Lyapunov characterizations of both properties. For time-varying and switched systems, such Lyapunov characterizations may not exist, and hence establishing the exact relationship between ISS and iISS remained an open problem, until now. In this paper, we solve this problem by providing a direct proof, i.e. without requiring Lyapunov characterizations, of the fact that ISS implies iISS, in a very general time-varying and switched-system context. In addition, we show how to construct suitable iISS gains based on the comparison functions that characterize the ISS property, and on bounds on the function f defining the system dynamics. When particularized to time-invariant systems, our assumptions are even weaker than existing ones. Another contribution is to show that for time-varying systems, local Lipschitz continuity of f in all variables is not sufficient to guarantee that ISS implies iISS. We illustrate application of our results on an example that does not admit an iISS-Lyapunov function."
format Artículos de Publicaciones Periódicas
acceptedVersion
author Haimovich, Hernán
Mancilla-Aguilar, J. L.
author_facet Haimovich, Hernán
Mancilla-Aguilar, J. L.
author_sort Haimovich, Hernán
title ISS implies iISS even for switched and time-varying systems (if you are careful enough)
title_short ISS implies iISS even for switched and time-varying systems (if you are careful enough)
title_full ISS implies iISS even for switched and time-varying systems (if you are careful enough)
title_fullStr ISS implies iISS even for switched and time-varying systems (if you are careful enough)
title_full_unstemmed ISS implies iISS even for switched and time-varying systems (if you are careful enough)
title_sort iss implies iiss even for switched and time-varying systems (if you are careful enough)
publishDate 2020
url http://ri.itba.edu.ar/handle/123456789/1859
work_keys_str_mv AT haimovichhernan issimpliesiissevenforswitchedandtimevaryingsystemsifyouarecarefulenough
AT mancillaaguilarjl issimpliesiissevenforswitchedandtimevaryingsystemsifyouarecarefulenough
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