Reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems based on an extended approach

Xie, Xiangpeng; Xie, Jun; Hu, Songlin

doi:10.1016/j.neucom.2015.09.038

Cited by 9 publications

(6 citation statements)

References 24 publications

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“…Then, T-S fuzzy system (30) is quadratically stabilizable via fuzzy control (27) for a prescribed performance index > 0, where…”

Section: Lemma 1 the Parameterised Linear Matrix Inequalitiesmentioning

confidence: 99%

“…Theorem 2 gives the relaxed LMI condition for the ∞ stability of the fuzzy system (30) and obtains the global T-S fuzzy controller by solving LMI. The fuzzy controller can guarantee the stability of the fuzzy system but not necessarily guarantee the stability of the original system.…”

Section: Lemma 1 the Parameterised Linear Matrix Inequalitiesmentioning

confidence: 99%

“…To illustrate the effectiveness of the designed controller based on T-S fuzzy model (30) for HGVs, the original nonlinear model (not the T-S fuzzy model) will be used to test the ∞ stability of the control system.…”

Section: Simulationsmentioning

confidence: 99%

“…Up to date, numerous theoretical studies on the T-S fuzzy control for nonlinear systems and ∞ control for the hypersonic vehicle have been conducted since the fuzzy controller was proposed in [25,26]. Most of these existing investigations use the Lyapunov stability theory to obtain the LMI conditions with lesser conservatism and further obtain the fuzzy controller for the closed-loop feedback system [11,[27][28][29][30]. Intensive theoretical results have also resulted in numerous engineering applications.…”

Section: Introductionmentioning

confidence: 99%

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T‐S Fuzzy Modelling and H_∞ Attitude Control for Hypersonic Gliding Vehicles

Zhang

Huang

Gao

2017

Mathematical Problems in Engineering

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This paper addresses the T-S fuzzy modelling and H∞ attitude control in three channels for hypersonic gliding vehicles (HGVs). First, the control-oriented affine nonlinear model has been established which is transformed from the reentry dynamics. Then, based on Taylor’s expansion approach and the fuzzy linearization approach, the homogeneous T-S local modelling technique for HGVs is proposed. Given the approximation accuracy and controller design complexity, appropriate fuzzy premise variables and operating points of interest are selected to construct the T-S homogeneous submodels. With so-called fuzzy blending, the original plant is transformed into the overall T-S fuzzy model with disturbance. By utilizing Lyapunov functional approach, a state feedback fuzzy controller has been designed based on relaxed linear matrix inequality (LMI) conditions to stable the original plants with a prescribed H∞ performance of disturbance. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed H∞ T-S fuzzy controller for the original attitude dynamics; the superiority of the designed T-S fuzzy controller compared with other local controllers based on the constructed fuzzy model is shown as well.

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“…Then, T-S fuzzy system (30) is quadratically stabilizable via fuzzy control (27) for a prescribed performance index > 0, where…”

Section: Lemma 1 the Parameterised Linear Matrix Inequalitiesmentioning

confidence: 99%

Section: Lemma 1 the Parameterised Linear Matrix Inequalitiesmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

T‐S Fuzzy Modelling and H_∞ Attitude Control for Hypersonic Gliding Vehicles

Zhang

Huang

Gao

2017

Mathematical Problems in Engineering

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“…Recently, by exploiting the idea of consensus averaging over a network , various multi‐agent optimization problems arising in the engineering community have been investigated by researchers . In the literature, remarkable results on stability analysis and controller synthesis for nonlinear multi‐agent systems have been reported based on the Takagi–Sugeno (T‐S) fuzzy model‐based approaches . For examples, Li et al designed a novel observer‐based adaptive sliding mode control approach of nonlinear Markovian jump systems with partly unknown transition probabilities and improved the performance of the considered systems.…”

Section: Introductionmentioning

confidence: 99%

Distributed mirror descent method for saddle point problems over directed graphs

Chen

Dong

et al. 2016

Complexity

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In this article, we consider a mini‐max multi‐agent optimization problem where multiple agents cooperatively optimize a sum of local convex–concave functions, each of which is available to one specific agent in a network. To solve the problem, we propose a distributed optimization method by extending classical mirror descent algorithms to the distributed setting. We obtain the convergence of the algorithm under wild conditions that the agent communication follows a directed graph and the related weighted matrices are row stochastic. In particular, when the weighted matrices are restricted to be doubly stochastic, we provide the explicit convergence rate of the algorithm by choosing the stepsize in a suitable way. The proposed algorithm can be viewed as a generalization of the subgradient projection methods since it utilizes a customized Bregman divergence instead of the usual Euclidean squared distance. Finally, some simulation results on a matrix game are presented to illustrate the performance of the algorithm. © 2016 Wiley Periodicals, Inc. Complexity 21: 178–190, 2016

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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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Reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems based on an extended approach

Cited by 9 publications

References 24 publications

T‐S Fuzzy Modelling and H_∞ Attitude Control for Hypersonic Gliding Vehicles

T‐S Fuzzy Modelling and H_∞ Attitude Control for Hypersonic Gliding Vehicles

Distributed mirror descent method for saddle point problems over directed graphs

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

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Reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems based on an extended approach

Cited by 9 publications

References 24 publications

T‐S Fuzzy Modelling and H∞ Attitude Control for Hypersonic Gliding Vehicles

T‐S Fuzzy Modelling and H∞ Attitude Control for Hypersonic Gliding Vehicles

Distributed mirror descent method for saddle point problems over directed graphs

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

Contact Info

Product

Resources

About

T‐S Fuzzy Modelling and H_∞ Attitude Control for Hypersonic Gliding Vehicles

T‐S Fuzzy Modelling and H_∞ Attitude Control for Hypersonic Gliding Vehicles

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