Generalized conformable operators: Application to the design of nonlinear observers

In this work, a pair of observers are proposed for a class of nonlinear systems whose dynamics involve a generalized differential operator that encompasses the conformable derivatives. A generalized conformable exponential stability function, based on this derivative, is introduced in order to prove...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 11; pp. 12952 - 12975
Main Authors Meléndez-Vázquez, Fidel, Fernández-Anaya, Guillermo, Muñóz-Vázquez, Aldo Jonathan, Hernández-Martínez, Eduardo Gamaliel
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
exponential stability
generalized conformable derivative
high-gain observer
lyapunov stability
nonlinear quadratic regulator
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Summary:In this work, a pair of observers are proposed for a class of nonlinear systems whose dynamics involve a generalized differential operator that encompasses the conformable derivatives. A generalized conformable exponential stability function, based on this derivative, is introduced in order to prove some Lyapunov-like theorems. These theorems help to verify the stability of the observers proposed, which is exponential in a generalized sense. The performance of the observation scheme is evaluated by means of numerical simulations. Moreover, a comparison of the results obtained with integer, fractional, and generalized conformable derivatives is made.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021749