New results on H∞ filtering for fuzzy systems with interval time-varying delays

Zhao, Yan; Gao, Huijun; Lam, James

doi:10.1016/j.ins.2011.01.032

Cited by 45 publications

(21 citation statements)

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“…(40) It is obvious that the condition (18) is followed by (40), which means that the FES (14) is stable with an H ∞ performance according to the Lyapunov stability theory. This completes the proof.…”

Section: A Delay-dependent H ∞ Performance Analysismentioning

confidence: 99%

“…Choosing d 1 = 3 and d 2 = 11 of time-delay, it is found that there is no feasible solution by the methods propseod in [40]- [42]. While applying Theorem 3.3 with δ 1 = δ 2 = 0, one indeed attains the H ∞ performance γ min = 7.4152.…”

Section: Theorem 33 Consider the Fuzzy-affine System (1) If There mentioning

confidence: 99%

“…In general, most of the approaches entail the construction of Lyapunov-Krasovskii functionals (LKFs) [31], and the employment of some comparatively tight techniques, such as Jensen's inequality [39], free-weighting matrix approach [29], delay-partitioning approach [40], inputoutput approach [41], or reciprocally convex approach [42], to derive numerically tractable stability analysis criteria for the time-delayed fuzzy systems. In retrospect, based on the freeweighting matrix approach, the authors in [29] investigated the problem of robust filter synthesis for fuzzy time-delay systems; By applying the delay-partitioning approach, the robust H ∞ filter analysis and synthesis problems for continuous-time fuzzy systems with state-delay were discussed in [40]; In [41], the authors dealt with the l 2 -l ∞ filtering problem for delayed fuzzy systems in an input-output framework; In [42], by utilizing the reciprocally convex approach, the authors considered the reliable filter design problem for discrete-time T-S fuzzy time-delay systems in a strict dissipativity sense. It is worth mentioning that the input-output approach relies es-sentially on the application of the model transformation, which is directly related to the selection of the LKFs.…”

mentioning

confidence: 99%

See 2 more Smart Citations

A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models

Wei

Qiu

Shi

et al. 2017

IEEE Trans. Syst. Man Cybern, Syst.

120

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Abstract-This paper proposes a novel delay-dependent approach to the piecewise-affine H-infinity filter design for discretetime state-delayed nonlinear systems. The nonlinear plant is expressed by a Takagi-Sugeno fuzzy-affine model and the state delay is considered to be time-varying with available lower and upper bounds. The purpose is to design an admissible filter that guarantees the asymptotic stability of the resulting filtering error system with a prescribed disturbance attenuation level in an H-infinity sense. By applying a new piecewisefuzzy Lyapunov-Krasovskii functional, combined with a novel summation inequality, improved reciprocally convex inequality and S-procedure, the H-infinity performance analysis criterion is firstly developed for the FES. Furthermore, the filter synthesis is carried out by some elegant convexification techniques. Finally, simulation examples are employed to confirm the effectiveness and less conservatism of the proposed methods.

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Section: A Delay-dependent H ∞ Performance Analysismentioning

confidence: 99%

Section: Theorem 33 Consider the Fuzzy-affine System (1) If There mentioning

confidence: 99%

mentioning

confidence: 99%

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A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models

Wei

Qiu

Shi

et al. 2017

IEEE Trans. Syst. Man Cybern, Syst.

120

View full text Add to dashboard Cite

show abstract

“…It is assumed that the premise variables do not depend on the disturbance. By using center-average defuzzifier, product interference and singleton fuzzifier [5][6][7][8][9][10][11][12][13][14]21,23,24,27,28], the T-S fuzzy dynamical NMJSs (2) can be inferred as follows:…”

Section: Remarkmentioning

confidence: 99%

“…It has been widely studied for many dynamical systems with different performance indexes, such as Kalman filtering [22], H ∞ filtering [23,24], H 2 filtering [25] and L 2 − L ∞ filtering [26], etc. Moreover, a great number of important results on stochastic Markovian jumping systems have been reported.…”

Section: Introductionmentioning

confidence: 99%

Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach

2015

Nonlinear Dyn

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In this paper, the non-fragile finite-time filtering problem is studied for a class of nonlinear Markovian jumping systems (NMJSs) with time delays and uncertainties. To design the mode-dependent nonfragile state filter, Takagi-Sugeno (T-S) fuzzy models are employed to represent the time-delayed and uncertain NMJSs. Then, based on the Lyapunov-Krasovskii functional, a sufficient condition is derived for the existence of a desired non-fragile H ∞ filter which also guarantees the finite-time boundness of the filtering error dynamical NMJSs. By this criterion, the approach to designing a non-fragile fuzzy filter is developed in terms of linear matrix inequalities. Finally, a numerical simulation is provided to illustrate the performance of the proposed method.

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Full and reduced‐order H_∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach

Aiss

Zoulagh

Hmamed

2021

Adaptive Control & Signal

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Summary This article addresses the issue of delay‐dependent H∞ filtering design for TakagiŮSugeno fuzzy time‐varying delay systems using the input–output approach. A three‐term approximation model has been used to transform the original system into two interconnected subsystems. Since the nonquadratic Lyapunov–Krasovskii functional requires to deal with the membership function's (MF) time derivative, upper‐bound inequalities have been added to the obtained conditions. Based on the scaled small gain theorem, nonquadratic Lyapunov–Krasovskii functional approach and considering the bounds of the MF time‐derivative, the H∞ full‐ and reduced‐order filters are designed and then formulated in terms of linear matrix inequalities. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.

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New results on H∞ filtering for fuzzy systems with interval time-varying delays

Cited by 45 publications

References 50 publications

A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models

A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models

Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach

Full and reduced‐order H_∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach

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New results on H∞ filtering for fuzzy systems with interval time-varying delays

Cited by 45 publications

References 50 publications

A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models

A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models

Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach

Full and reduced‐order H∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach

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Full and reduced‐order H_∞ filtering of Takagi–Sugeno fuzzy time‐varying delay systems: Input–output approach