Robust fuzzy Lyapunov stabilization for uncertain and disturbed Takagi–Sugeno descriptors

Bouarar, Tahar; Guelton, Kevin; Manamanni, Noureddine

doi:10.1016/j.isatra.2010.06.003

Cited by 70 publications

(34 citation statements)

References 34 publications

(82 reference statements)

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“…Nonetheless, the quadratic approach presents serious limitations because its solutions are inherently pessimistic, i.e., there are stable or stabilizable models which do not have a quadratic solution (see [10] and references therein). Conservativeness comes from different sources: the type of TS model [11,12], the way the membership functions are dropped-off to obtain LMI expressions [13][14][15], the integration of membership-function information [16,17], or the choice of Lyapunov function [18,19]. This work is concerned with a relaxation in the latter sense which demands a change of perspective from global to local conditions.…”

Section: Introductionmentioning

confidence: 99%

Non-quadratic local stabilization for continuous-time Takagi–Sugeno models

Guerra¹,

Bernal²,

Guelton³

et al. 2012

Fuzzy Sets and Systems

120

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This paper is concerned with non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models. The well-known problem of handling time-derivatives of membership functions (MFs) as to obtain conditions in the form of linear matrix inequalities (LMIs) is overcome by reducing global goals to the estimation of a region of attraction. Instead of parallel distributed compensation (PDC), a non-PDC control law is proposed according to the non-quadratic nature of the Lyapunov function. Examples are provided to show the advantages over the quadratic and some non-quadratic approaches.

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Section: Introductionmentioning

confidence: 99%

Non-quadratic local stabilization for continuous-time Takagi–Sugeno models

Guerra¹,

Bernal²,

Guelton³

et al. 2012

Fuzzy Sets and Systems

120

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“…A "virtual dynamics" is introduced in the output error ( ) to avoid the crossing terms resulting from the observer's gains and system matrices multiplication [25]. This latter can be expressed as given by (34), where 0 is a zero matrix.…”

Section: Fig3 Tracking Fault Tolerant Controller Design Methodologymentioning

confidence: 99%

Robust fault tolerant tracking controller design for a VTOL aircraft

Chadli

Aouaouda

Karimi

et al. 2013

Journal of the Franklin Institute

115

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Abstract-This paper deals with the fault tolerant control (FTC) design for a Vertical Takeoff and Landing (VTOL) aircraft subject to external disturbances and actuator faults. The aim is to synthesize a fault tolerant controller ensuring trajectory tracking for the nonlinear uncertain system represented by Takagi-Sugeno (T-S) model. In order to design the FTC law, a proportional integral observer (PIO) is adopted which estimate both of the faults and the faulty system states. Based on Lyapunov theory and ℒ 2 optimization, the trajectory tracking performance and the stability of the closed loop system are analyzed. Sufficient conditions are obtained in terms of linear matrix inequalities (LMI). Simulation results show that the proposed controller is robust with respect to uncertainties on the mechanical parameters that characterize the model and secures global convergence.

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“…According to (8), to avoid the crossing terms resulting from the observer's gains 1 i H and system matrices ( i C and i D ) multiplication, we introduce a "virtual dynamics" in the output error ( ) y et [11] [12]. This latter can be expressed as:…”

Section: Fault Tolerant Controller Designmentioning

confidence: 99%

Trajectory tracking fault tolerant controller design for Takagi-Sugeno systems subject to actuator faults

Bouarar¹,

Marx²,

Maquin³

et al. 2011

2011 International Conference on Communications, Computing and Control Applications (CCCA)

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Abstract-This paper investigates the problem of fault tolerant control (FTC) design for nonlinear Takagi-Sugeno (T-S) models with measurable premise variables. The idea is to synthesize a fault tolerant controller ensuring state trajectory tracking. Based on Lyapunov theory, new less conservative approaches a r e proposed in term of Linear Matrix Inequality (LMI). A P I observer is needed to estimate simultaneously the faults and the faulty system states in order to reconfigure the FTC la w. A numerical example is considered to compare the conservatism of the proposed FTC approaches with the existing one and to illustrate the effectiveness of the FTC technique vs. the classical controller design methodology.

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Robust fuzzy Lyapunov stabilization for uncertain and disturbed Takagi–Sugeno descriptors

Cited by 70 publications

References 34 publications

Non-quadratic local stabilization for continuous-time Takagi–Sugeno models

Non-quadratic local stabilization for continuous-time Takagi–Sugeno models

Robust fault tolerant tracking controller design for a VTOL aircraft

Trajectory tracking fault tolerant controller design for Takagi-Sugeno systems subject to actuator faults

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