Observer Design For Takagi-Sugeno Descriptor System With Lipschitz Constraints

Ilhem, Kilani; Jabri, Dalel; Saloua, Bel Hadj Ali Naoui; Abdelkrim, Mohamed Naceur

doi:10.5121/ijics.2012.2202

Cited by 12 publications

(10 citation statements)

References 12 publications

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“…with α 1 = 8.29, α 2 = 552.59, α 3 = 1.38, α 4 = 92.10, α 5 = 11.45, α 6 = 9.21 * 10 −9 , α 7 = 5.53 * 10 −8 Note that, the application of the proposed observer (16) for heat exchanger pilot process requires that the above model (44) takes the form (15). To do so, considering the following:…”

Section: Application To a Heat Exchanger Systemmentioning

confidence: 99%

“…We may cite [8], [9], [10], [11], [12], [13]. For nonlinear descriptor systems described by T-S models, several developments exist for continuous-time case [14], [15], [16], [17] and for discrete-time one [18], [19]. Moreover, many other works dealing with observer design in explicit form called Proportional Integral Observer were also proposed for implicit T-S models.…”

Section: Introductionmentioning

confidence: 99%

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Observer design for a class of Takagi-Sugeno descriptor systems with Lipschitz constraints

Louzimi¹,

Assoudi²,

Soulami³

et al. 2016

ams

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This paper deals with the problem of the state estimation for both continuous and discrete time nonlinear descriptor systems described by Takagi-Sugeno (TS) structure with unmeasurable premise variables which satisfying Lipschitz conditions. Indeed, the T-S fuzzy observers are synthesized in explicit forms to estimate exactly the unknown descriptor's states. The idea of the proposed result is based on the separation between dynamic and static relations in the T-S descriptor model. Firstly, the method used to decompose the dynamic equations of the algebraic equation is developed. Secondly, the fuzzy observer designs satisfying Lipschitz conditions and permitting to estimate the unknown states are established for both continuous and discrete time cases. The convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of only one Linear Matrix Inequalitie (LMI). Finally, an application to a descriptor model of a heat exchanger pilot process is given in order to illustrate the validity and applicability of the proposed method.

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Section: Application To a Heat Exchanger Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observer design for a class of Takagi-Sugeno descriptor systems with Lipschitz constraints

Louzimi¹,

Assoudi²,

Soulami³

et al. 2016

ams

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show abstract

“…A new line of reflection based on the TS approximation has given the control structures which generally optimize the prescribed control loop performances (Guerra et al (2005), Lin et al (2006), Taniguchi et al (2000), Wang et al (2004)). Moreover, LMI-based design techniques for the fuzzy descriptor observers have been investigated (Ilhem et al (2012), Krokavec and A. Filasová (2014b)) to solve the problem of observer based control.…”

Section: Introductionmentioning

confidence: 99%

Design of PD Observer-Based Fault Estimator for a Class of Takagi-Sugeno Descriptor Systems∗∗The work presented in this paper was supported by VEGA, the Grant Agency of the Ministry of Education and the Academy of Science of Slovak Republic, under Grant No. 1/0348/14. This support is very gratefully acknowledged.

Krokavec

Filasová

2015

IFAC-PapersOnLine

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A generalized approach to design a proportional and derivative system faults fuzzy observer for continuous-time nonlinear systems described in the Takagi-Sugeno descriptor statespace form is presented in the paper. Considering measurable premise variables, the problem addressed is formulated as an enhanced concept to descriptor systems design, implying the asymptotic convergence both the state observer error as fault estimate error. Presented in the sense of the second Lyapunov method, an associated structure of linear matrix inequalities is outlined to possess the global observer asymptotic dynamic properties with compiling the local insiders by inference through the membership functions equal those of the system model. The proposed design conditions are verified by simulations in the numerical illustrative example.

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“…Adapting the descriptor observer design principle [7], the first result giving sufficient design conditions, but for linear time-delay systems, can be found in [8]. Reflecting the same problems concerning the observers for descriptor time-delay nonlinear systems represented by TS fuzzy models, an LMI method was presented in [9], but a hint of this methodology can be found only in [10].…”

Section: Introductionmentioning

confidence: 99%