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On the Continuous Finite-Time Stabilization of the Double Integrator

dc.contributor.authorZavala-Rio, Arturo
dc.contributor.authorSánchez Ramírez, Tonámetl
dc.contributor.authorZamora Gómez, Griselda Ivone
dc.date.accessioned2023-10-24T19:43:22Z
dc.date.available2023-10-24T19:43:22Z
dc.date.issued2022
dc.identifier.urihttp://hdl.handle.net/11627/6485
dc.description.abstract"Continuous finite-time stabilization is often treated under the analytical framework of homogeneity and has been frequently illustrated in the context of the feedback control of the double integrator. For such a simple system, the simplest considered continuous finite-time controller is composed of gained (proportional) exponentially weighted position and velocity error correction terms, with the exponential weights generally less than unity and constrained to satisfy a particular relation among them under homogeneity. What happens for less-than-unity exponential weights that do not satisfy such a homogeneity-based relation? Does the finite-time stabilization hold? Through a Lyapunov function--based study, we analyze and give more concrete answers to such questions than those partially provided by previous studies on the topic. We do find a more exhaustive spectrum of the exponential weights that give rise to finite-time stability of the trivial solution. Other types of stability properties are further found to take place for less-than-or-equal-to-unity exponential weights. Moreover, through complementary analysis, local or ultimate behavior of the system solutions is further characterized. The analytical findings are further illustrated through computer simulations."es_MX
dc.language.isoenges_MX
dc.publisherSIAMes_MX
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectContinuous finite-time controles_MX
dc.subjectFinite-time stability/stabilizationes_MX
dc.subjectExponential stability with respect to a homogeneous normes_MX
dc.subjectDouble integratores_MX
dc.subject.classificationArea::CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA::MATEMÁTICAS::INVESTIGACIÓN OPERATIVA::SISTEMAS DE CONTROLes_MX
dc.titleOn the Continuous Finite-Time Stabilization of the Double Integratores_MX
dc.typearticlees_MX


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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 Internacional