Global stability results for switched systems based on weak Lyapunov functions

"In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbationlike one. Most stability results for perturbed systems are based on the use of s...

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Autores principales: Mancilla-Aguilar, J. L., Haimovich, Hernán, García Galiñanes, Rafael
Formato: Artículos de Publicaciones Periódicas nfo:eu-repo/semantics/acceptedVersion
Lenguaje:Inglés
Publicado: 2019
Materias:
SISTEMAS DINAMICOS
ESTABILIDAD
METODO LYAPUNOV
SISTEMAS DE CONMUTACION
Acceso en línea:http://ri.itba.edu.ar/handle/123456789/1725
Aporte de:
Repositorio Institucional Instituto Tecnológico de Buenos Aires (ITBA) de Instituto Tecnológico de Buenos Aires (ITBA)
id I32-R138-123456789-1725
record_format dspace
spelling I32-R138-123456789-17252022-12-07T13:06:08Z Global stability results for switched systems based on weak Lyapunov functions Mancilla-Aguilar, J. L. Haimovich, Hernán García Galiñanes, Rafael SISTEMAS DINAMICOS ESTABILIDAD METODO LYAPUNOV SISTEMAS DE CONMUTACION "In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbationlike one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-timevarying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm." 2019-08-21T16:20:50Z 2019-08-21T16:20:50Z 2017-06 Artículos de Publicaciones Periódicas nfo:eu-repo/semantics/acceptedVersion 0018-9286 http://ri.itba.edu.ar/handle/123456789/1725 en info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2016.2627622 info:eu-repo/grantAgreement/ANPCyT/PICT /2013-0852/AR. Ciudad Autónoma de Buenos Aires info:eu-repo/grantAgreement/ANPCyT/PICT /2014-2599/AR. Ciudad Autónoma 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 DINAMICOS
ESTABILIDAD
METODO LYAPUNOV
SISTEMAS DE CONMUTACION
spellingShingle SISTEMAS DINAMICOS
ESTABILIDAD
METODO LYAPUNOV
SISTEMAS DE CONMUTACION
Mancilla-Aguilar, J. L.
Haimovich, Hernán
García Galiñanes, Rafael
Global stability results for switched systems based on weak Lyapunov functions
topic_facet SISTEMAS DINAMICOS
ESTABILIDAD
METODO LYAPUNOV
SISTEMAS DE CONMUTACION
description "In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbationlike one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-timevarying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm."
format Artículos de Publicaciones Periódicas
nfo:eu-repo/semantics/acceptedVersion
author Mancilla-Aguilar, J. L.
Haimovich, Hernán
García Galiñanes, Rafael
author_facet Mancilla-Aguilar, J. L.
Haimovich, Hernán
García Galiñanes, Rafael
author_sort Mancilla-Aguilar, J. L.
title Global stability results for switched systems based on weak Lyapunov functions
title_short Global stability results for switched systems based on weak Lyapunov functions
title_full Global stability results for switched systems based on weak Lyapunov functions
title_fullStr Global stability results for switched systems based on weak Lyapunov functions
title_full_unstemmed Global stability results for switched systems based on weak Lyapunov functions
title_sort global stability results for switched systems based on weak lyapunov functions
publishDate 2019
url http://ri.itba.edu.ar/handle/123456789/1725
work_keys_str_mv AT mancillaaguilarjl globalstabilityresultsforswitchedsystemsbasedonweaklyapunovfunctions
AT haimovichhernan globalstabilityresultsforswitchedsystemsbasedonweaklyapunovfunctions
AT garciagalinanesrafael globalstabilityresultsforswitchedsystemsbasedonweaklyapunovfunctions
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