A membership-function-dependent approach for stability analysis and controller synthesis of Takagi–Sugeno models

Bernal, Miguel; Guerra, Thierry Marie; Kruszewski, Alexandre

doi:10.1016/j.fss.2009.02.005

Cited by 96 publications

(39 citation statements)

References 20 publications

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“…However, there is a drawback of heavy computational burden due to the large number of the variables and conditions. For the method proposed in [41], unfortunately, the operating domain partition heavily depends on the membership function shape and order relation is not a very accurate membership function shape information. In [45,47], the information of membership functions is mainly the global/local boundary information of the membership functions, the numerical relation among all the membership functions was not considered.…”

Section: Introductionmentioning

confidence: 99%

“…In [45,47], the information of membership functions is mainly the global/local boundary information of the membership functions, the numerical relation among all the membership functions was not considered. In this paper, an alternative stability analysis approach using membership function information is proposed that the operating domain of the PFMB control system is partitioned into several sub-domains uniformly which makes the operating domain partition to be more flexible comparing with [41]. Based on the operating domain partition, the regional information of the membership functions are extracted in the subdomains.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Relaxed stability conditions for polynomial‐fuzzy‐model‐based control system with membership function information

Zhao

Lam

Song

et al. 2017

IET Control Theory & Applications

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relaxed stability conditions for polynomial‐fuzzy‐model‐based control system with membership function information

Zhao

Lam

Song

et al. 2017

IET Control Theory & Applications

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“…However, it is recognized that the common quadratic Lyapunov function is independent of membership functions, which may lead to conservativeness. To further reduce the conservatism in stability analysis, several non-quadratic Lyapunov functions have been proposed, such as piecewise Lyapunov functions [4,5,22] and fuzzy Lyapunov functions [1,2,8,12,15,17,18].…”

Section: Introductionmentioning

confidence: 99%

Relaxed stability conditions for interval type-2 fuzzy-model-based control systems

Zhao¹,

Xiao²,

Ding³

et al. 2014

Kybernetika

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“…Anyway, unless fuzzy-Lyapunov functions are used (Tanaka, Hori and Wang, 2003;Jaadari, 2013), the basins of attraction proved with LMI's are not membership dependent. This drawback has been addressed in some works like Sala and Ariño (2007b);Bernal, Guerra and Kruszewski (2009), which add membership function information to the LMI problem. Nevertheless, this is an inherent price to pay in extending linear tools for doing nonlinear control.…”

Section: Discussionmentioning

confidence: 99%

“…In addition, the works presented in the references Sala and Ariño (2007b);Bernal, Guerra and Kruszewski (2009), focus on the problem of conservativeness when assuming state independence in the membership functions, mentioned in the above section, and propose ideas in order to add the membership information to the LMI problem.…”

Section: Further Developmentsmentioning

confidence: 99%

Contributions to fuzzy polynomial techniques for stability analysis and control

Pérez¹,

Luis²

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Support from the French Laboratory LAMIH UMR CNRS8530 from the Université de Valenciennes et du Hainaut-Cambrésis is also acknowledged, both for accepting the author in its facilities as pre-doctoral stay and for its valuable collaboration sharing knowledge and data for the experimental applications presented on this thesis.The author thanks also the Control of Complex Systems Group from the Universitat Politècnica de València for the use of the group's infrastructure, in particular computational resources (Carraixet server).To all the people who decided getting out of my life by their own decision, because their absence provided me with more time for working and, of course, to you, expensive reader. AgradecimientosHan sido cuatro duros, pero a la vez amenos, años de trabajo para dar su fruto en esta tesis doctoral. Por lo tanto, hay muchas personas que, en mayor o menor medida, han contribuido de alguna forma a que este trabajo se haya llevado a buen puerto y voy a tener que rogar me disculpen por no haber sido capaz de acordarme de todos/as en estas lineas. En primer lugar, como no podría ser de otra forma, quiero agradecer a mi director de tesis, Antonio Sala, por todo lo que se le presupone a un director (transferencia de conocimiento en la materia, disponibilidad, supervisión del trabajo, trazado de guias principales, etc) y sobre todo por lo que no se le presupone: humildad, cercanía, paciencia infinita, sinceridad y consejos, incluso sobre aspectos de la vida que están fuera del ambito exclusivo del doctorado. Por ser verdaderamente un profesor para mi, gracias Antonio.Asimismo, quiero agradecer profundamente a Carlos Ariño por estar siempre disponible para explicarme cosas, aportar ideas y revisar mi trabajo, cuando oficialmente no tenía ninguna obligación para ello.Tampoco sería justo que en estas lineas me olvidara de Nacho Peñarrocha, mi director de proyecto final de carrera, a quien no pude agradecer en su momento por reglas de formato en el manuscrito. Probablemente, si Nacho no hubiera impartido las prácticas de Sistemas Automáticos en 2006, no me hubiera dirigido el PFC, o no me hubiera animado a solicitar la beca FPI, no estaría escribiendo estas lineas en mi tesis ahora.Espero, en algún momento y de alguna manera, ser capaz de devolveros a los tres todo el esfuerzo y dedicación que empleasteis en mi formación como investigador, como ingeniero y como persona.En segundo lugar, estoy especialmente agradecido a Thierry-Marie Guerra por haberme permitido trabajar tres meses en las instalaciones del LAMIH y tratarme como un investigador invitado en lugar de como un estudiante predoctoral. De la misma forma, quiero agradecer a Jimmy Lauber por aceptar ix x AGRADECIMIENTOS supervisar mi trabajo, colaborar conmigo y, para ello, sacar tiempo de donde no tenía.En tercer lugar, quiero agradecer de forma especial a Alejandro Vignoni, quien ha sido compañero de fatigas durante estos ultimos tres años y a quien le debo el aprender a moverme por el mundo, perdiendo el miedo a vivir fuera de mi termo particular....

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A membership-function-dependent approach for stability analysis and controller synthesis of Takagi–Sugeno models

Cited by 96 publications

References 20 publications

Relaxed stability conditions for polynomial‐fuzzy‐model‐based control system with membership function information

Relaxed stability conditions for polynomial‐fuzzy‐model‐based control system with membership function information

Relaxed stability conditions for interval type-2 fuzzy-model-based control systems

Contributions to fuzzy polynomial techniques for stability analysis and control

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