Global stability results for switched systems based on weak Lyapunov functions

Mancilla-Aguilar, J. L.; Haimovich, Hernán; García Galiñanes, Rafael

Artículo de Publicación Periódica:
Global stability results for switched systems based on weak Lyapunov functions

dc.contributor.author	Mancilla-Aguilar, J. L.
dc.contributor.author	Haimovich, Hernán
dc.contributor.author	García Galiñanes, Rafael
dc.date.accessioned	2019-08-21T16:20:50Z
dc.date.available	2019-08-21T16:20:50Z
dc.date.issued	2017-06
dc.description.abstract	"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."	en
dc.identifier.issn	0018-9286
dc.identifier.uri	http://ri.itba.edu.ar/handle/123456789/1725
dc.language.iso	en	en
dc.relation	info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2016.2627622
dc.relation	info:eu-repo/grantAgreement/ANPCyT/PICT /2013-0852/AR. Ciudad Autónoma de Buenos Aires
dc.relation	info:eu-repo/grantAgreement/ANPCyT/PICT /2014-2599/AR. Ciudad Autónoma de Buenos Aires
dc.subject	SISTEMAS DINAMICOS	es
dc.subject	ESTABILIDAD	es
dc.subject	METODO LYAPUNOV	es
dc.subject	SISTEMAS DE CONMUTACION	es
dc.title	Global stability results for switched systems based on weak Lyapunov functions	en
dc.type	Artículos de Publicaciones Periódicas	es
dc.type	nfo:eu-repo/semantics/acceptedVersion
dspace.entity.type	Artículo de Publicación Periódica
itba.description.filiation	Fil: Mancilla-Aguilar, J. L. Instituto Tecnológico de Buenos Aires; Argentina.
itba.description.filiation	Fil: García Galiñanes, Rafael. Instituto Tecnológico de Buenos Aires; Argentina.
itba.description.filiation	Fil: Haimovich, Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
itba.description.filiation	Fil: Haimovich, Hernán. Universidad Nacional de Rosario; Argentina.