State and fault estimation based on fuzzy observer for a class of Takagi-Sugeno singular models

Ouarid, Kaoutar; Essabre, Mohamed; Assoudi, Abdellatif El; Yaagoubi, El Hassane El

doi:10.11591/ijeecs.v25.i1.pp172-182

Cited by 4 publications

(4 citation statements)

References 25 publications

(34 reference statements)

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“…it follows that (46) is equivalent to (29). Finally, according to Lyapunov stability theory, if the LMI conditions (29) are satisfied, the ( 24) is exponentially stable.…”

Section: ❒ Issn: 2088-8708mentioning

confidence: 98%

“…Developing an UIO for T-S fuzzy systems satisfying Lipschitz conditions is the aim of the work presented in [28]. In [29] the authors used the result obtained in [27] to develop a new approach making it possible to estimate simultaneously both non-measurable states and unknown faults in the actuators and sensors for T-S implicit model with MPV.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Essabre

Hmaiddouch

Assoudi

et al. 2023

IJECE

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<p>Recent years have seen a great deal of interest in implicit nonlinear systems, which are used in many different engineering applications. This study is dedicated to presenting a new method of fuzzy unknown inputs observer design to estimate simultaneously both non-measurable states and unknown inputs of continuous-time nonlinear implicit systems defined by Takagi-Sugeno (T-S) models with unmeasurable premise variables. The suggested observer is based on the singular value decomposition approach and rewritten the continuous-time T-S implicit models into an augmented fuzzy system, which gathers the unknown inputs and the state vector. The exponential convergence condition of the observer is established by using the Lyapunov theory and linear matrix inequalities are solved to determine the gains of the observer. Finally, the effectiveness of the suggested method is then assessed using a numerical application. It demonstrates that the estimated variables and the unknown input converge to the real variables accurately and quickly (less than 0.5 s).</p>

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“…it follows that (46) is equivalent to (29). Finally, according to Lyapunov stability theory, if the LMI conditions (29) are satisfied, the ( 24) is exponentially stable.…”

Section: ❒ Issn: 2088-8708mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Essabre

Hmaiddouch

Assoudi

et al. 2023

IJECE

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show abstract

“…Theorem 4.2: Let (𝑉, 𝑁 ̃𝑓, 𝛥 𝑐 ) be a FRNS with 𝛥 𝑐 is upper semi-continuous. Define: 𝑞 𝛼 (ⱱ 1 ) = 𝑖𝑛𝑓{𝑡 > 0, 𝑁 ̃𝑓(ⱱ 1 , 𝑡) < 𝛼} for 0 < 𝛼 < 1 (6) and 𝑄={𝑞 𝛼 (•), 0 < 𝛼 < 1} then (𝑉, 𝑄) is a GSQNF.…”

Section: Creating Space Of Quasinorm Familymentioning

confidence: 99%

Some remarks concerning on a fuzzy real normed space

Mohammedali

2022

IJEECS

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In mathematics, computer science, statistics, and other fields, the notion of fuzzy metric and fuzzy normed is crucial. Finding an acceptable fuzzy metric or norm for making some measurements can solve a lot of difficulties. In the sense of Mohammedali, fuzzy real normed spaces (FRNS) are the issue of this paper. Real normed and fuzzy real normed are advanced together with a ground-breaking analysis of their interactions. The structure of FRNS in terms of families of sublinear functional is established. After investigating some properties of "sublinear functional" that corresponding to an FRN, the concept of the family of star sublinear funtional based on the popular t-conorm (a parameter some families) is introduced with proved that a descending and separating family of star sublinear functional, denoted by produces a FRNS. In addition, the concept of generating space of quasinorm and quasi-norm family (GSQNF) has been presented. Furthermore, the decomposition theorem of a FRN into a family of quasinorm is formulated. The correlation between FRNS and the quasinorm family's generating space is explored and demonstrated.

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“…Bouassem et al [12] suggested another technique based on the separation between static and dynamic relations in the T-S implicit system to estimate both the system state and the UIs concomitantly. This approach allowed the estimation of both nonmeasurable states and unknown faults in the actuators and sensors for a class of continuous-time T-S implicit models in [13]. Louzimi et al [14], a design of an UIO is proposed for a class of continuous-time T-S implicit systems satisfying the Lipschitz conditions.…”

Section: Introductionmentioning

confidence: 99%

Design of unknown input observer for discrete-time Takagi Sugeno implicit systems with unmeasurable premise variables

Essabre

Hmaiddouch²,

Assoudi³

et al. 2023

Bulletin EEI

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In this study, an unknown input observer (UIO) is developed in explicit form to estimate unmeasurable states and unknown inputs (UIs) for nonlinear implicit systems represented by the discrete-time Takagi-Sugeno implicit systems (DTSIS) in the case of unmeasurable premise variables. The method employed is based on singular value decomposition (SVD) and augmenting the state vector, which is formed partly by the system state and partly by the UIs. The convergence of the augmented state estimation error is provided by a Lyapunov function ending with solving the linear matrix inequalities (LMI). An application to a model of the rolling disc is considered to evaluate the effectiveness of the developed approach. It appears that estimated variables converge to the true variables quickly and accurately.

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State and fault estimation based on fuzzy observer for a class of Takagi-Sugeno singular models

Cited by 4 publications

References 25 publications

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Some remarks concerning on a fuzzy real normed space

Design of unknown input observer for discrete-time Takagi Sugeno implicit systems with unmeasurable premise variables

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