Geometric approach to robust stability analysis of linear parameter-varying systems: computational trade-offs between the exact and the simplex convex hulls

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dc.creatorIgor Vieira Pereira
dc.creatorFernando de Oliveira Souza
dc.creatorLeonardo Amaral Mozelli
dc.date.accessioned2025-05-26T12:51:34Z
dc.date.accessioned2025-09-09T00:52:49Z
dc.date.available2025-05-26T12:51:34Z
dc.date.issued2023
dc.identifier.doihttps://doi.org/10.1016/j.amc.2023.128017
dc.identifier.issn0096-3003
dc.identifier.urihttps://hdl.handle.net/1843/82487
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.relation.ispartofApplied mathematics and computation
dc.rightsAcesso Restrito
dc.subjectLiapunov, Funções de
dc.subjectSistemas lineares
dc.subject.otherLinear parameter-varying systems
dc.subject.otherParameter dependent lyapunov functions
dc.subject.otherPolytopic geometry
dc.subject.otherComputational effort
dc.titleGeometric approach to robust stability analysis of linear parameter-varying systems: computational trade-offs between the exact and the simplex convex hulls
dc.typeArtigo de periódico
local.citation.spage128017
local.citation.volume451
local.description.resumoRobust stability is investigated for continuous-time, affine, Linear Parameter-Varying (LPV) models, with bounded variation rates of uncertainty. Towards this end, affine Parameter Dependent Lyapunov Functions (PDLF) are considered to certificate stability in the Lyapunov sense. In the literature, the search for PDLFs amounts to a non conservative Linear Matrix Inequality (LMI) problem, at expense of a factorial growth in its complexity. Remedies to overcome this complexity have been proposed recently, exploiting geometrical aspects of the problem, however, they can be conservative. This paper presents new stability tests that are a trade-off between the exact and the fastest solutions. We offer an analytical procedure to indicate when the proposed tests are prone to reduce conservativeness. Also, a simple procedure is introduced to possibly improve existing and new tests, without impacts on the computation effort. Numerical simulations illustrate the improvements of the proposed strategies.
local.publisher.countryBrasil
local.publisher.departmentENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
local.publisher.initialsUFMG
local.url.externahttps://www.sciencedirect.com/science/article/pii/S0096300323001868

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