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New Stability Criterion for Continuous-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delay

Published on Apr 1, 2019in IEEE Transactions on Systems, Man, and Cybernetics7.35
· DOI :10.1109/tcyb.2018.2801795
Likui Wang2
Estimated H-index: 2
(Nanchang Hangkong University),
Hak-Keung Lam43
Estimated H-index: 43
('KCL': King's College London)
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Abstract
In this technical paper, a new Lyapunov–Krasovskii functional (LKF) is designed to study the stability of continuous-time Takagi–Sugeno fuzzy systems with time-varying delay. The integrand of the LKF depends on integral variable and time {t} which can help to reduce the number of linear matrix inequalities (LMIs). Then, a new stability criterion is derived by analyzing the sign of the time derivatives of membership functions. Compared with the existing results, larger delay bounds can be obtained by applying the new criterion. In the end, two examples show the effectiveness of the conclusions.
  • References (19)
  • Citations (6)
Cite
References19
Newest
Xiangpeng Xie12
Estimated H-index: 12
(NUPT: Nanjing University of Posts and Telecommunications),
Dong Yue48
Estimated H-index: 48
(NUPT: Nanjing University of Posts and Telecommunications)
+ 1 AuthorsChen Peng27
Estimated H-index: 27
(SHU: Shanghai University)
The augmented multi-indexed matrix approach acts as a powerful tool in reducing the conservatism of control synthesis of discrete-time Takagi–Sugeno fuzzy systems. However, its computational burden is sometimes too heavy as a tradeoff. Nowadays, reducing the conservatism whilst alleviating the computational burden becomes an ideal but very challenging problem. This paper is toward finding an efficient way to achieve one of satisfactory answers. Different from the augmented multi-indexed matrix a...
Zhiguang Feng13
Estimated H-index: 13
(HEU: Harbin Engineering University),
Wei Xing Zherzg54
Estimated H-index: 54
(USYD: University of Sydney)
In this paper, the stability analysis problem of Takagi–Sugeno fuzzy systems with time-varying delay is investigated. By utilizing the Wirtinger-based integral inequality and the improved reciprocally convex combination technique, an improved stability condition is derived in terms of linear matrix inequalities. A numerical example is given to demonstrate the efficiency of the obtained result.
Published on Jan 1, 2017in IEEE Transactions on Automatic Control5.09
Xiaodi Li10
Estimated H-index: 10
(SDNU: Shandong Normal University),
Shiji Song23
Estimated H-index: 23
(THU: Tsinghua University)
The stabilization problem of delay systems is studied under the delay-dependent impulsive control. The main contributions of this technical note are that, for one thing, it shows that time delays in impulse term may contribute to the stabilization of delay systems, that is, a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks; for another, it shows the robustness of impulsi...
Published on Dec 1, 2016in Information Sciences5.52
O. M. Kwon23
Estimated H-index: 23
(CBNU: Chungbuk National University),
Myeong-Jin Park22
Estimated H-index: 22
(CBNU: Chungbuk National University)
+ 1 AuthorsSang-Moon Lee42
Estimated H-index: 42
(KNU: Kyungpook National University)
This paper is concerned with the problem of stability and stabilization for Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, sufficient conditions for ensuring the asymptotic stability and stabilization of the concerned fuzzy systems have been derived within the framework of linear matrix inequalities (LMIs). The advantage and effectiveness of the proposed criteria will be shown through the comparison of maximum delay bounds w...
Published on May 1, 2016in IEEE Transactions on Automatic Control5.09
Xiaojie Su22
Estimated H-index: 22
(Chongqing University),
Peng Shi106
Estimated H-index: 106
(University of Adelaide)
+ 1 AuthorsYongduan Song26
Estimated H-index: 26
(Chongqing University)
In this note, the fault detection filtering problem is solved for nonlinear switched stochastic system in the T-S fuzzy framework. Our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with Brownian motion. Based on observer-based fault detection fuzzy filter as a residual generator, the proposed fault detection is formulated as a fuzzy filtering problem. By the utilization of the average dwell time technique and the piecewise Ly...
Rathinasamy Sakthivel33
Estimated H-index: 33
(SKKU: Sungkyunkwan University),
Subramaniam Selvi7
Estimated H-index: 7
(Chettinad College of Engineering and Technology)
+ 1 AuthorsPeng Shi106
Estimated H-index: 106
(HEU: Harbin Engineering University)
This paper is concerned with the problem of reliable mixed {H} _{\boldsymbol {\infty }}and passivity-based control for a class of stochastic Takagi-Sugeno (TS) fuzzy systems with Markovian switching and probabilistic time varying delays. Different from the existing works, the {H} _{\boldsymbol {\infty }}and passivity control problem with probabilistic occurrence of time-varying delays and actuator failures is considered in a unified framework, which is more general in some practical situat...
Published on 2015in IEEE Transactions on Fuzzy Systems8.76
Zhang Huaguang51
Estimated H-index: 51
(NU: Northeastern University),
Jilie Zhang4
Estimated H-index: 4
(NU: Northeastern University)
+ 1 AuthorsYanhong Luo (NU: Northeastern University)
In this paper, a new online scheme is presented to design the optimal coordination control for the consensus problem of multiagent differential games by fuzzy adaptive dynamic programming, which brings together game theory, generalized fuzzy hyperbolic model (GFHM), and adaptive dynamic programming. In general, the optimal coordination control for multiagent differential games is the solution of the coupled Hamilton-Jacobi (HJ) equations. Here, for the first time, GFHMs are used to approximate t...
Published on Dec 1, 2014in Automatica6.36
Xiaojie Su22
Estimated H-index: 22
(Chongqing University),
Ligang Wu57
Estimated H-index: 57
(HIT: Harbin Institute of Technology)
+ 1 AuthorsYongduan Song26
Estimated H-index: 26
(Chongqing University)
This paper investigates the problem of Hankel-norm output feedback controller design for a class of T-S fuzzy stochastic systems. The full-order output feedback controller design technique with the Hankel-norm performance is proposed by the fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a p...
Xiangpeng Xie12
Estimated H-index: 12
(NUPT: Nanjing University of Posts and Telecommunications),
Dong Yue48
Estimated H-index: 48
(NUPT: Nanjing University of Posts and Telecommunications)
+ 1 AuthorsXun-Lin Zhu2
Estimated H-index: 2
(Zhengzhou University)
Fernando O. Souza14
Estimated H-index: 14
(UFMG: Universidade Federal de Minas Gerais),
Víctor Costa da Silva Campos5
Estimated H-index: 5
(UFMG: Universidade Federal de Minas Gerais),
Reinaldo M. Palhares28
Estimated H-index: 28
(UFMG: Universidade Federal de Minas Gerais)
Abstract This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Kr...
Cited By6
Newest
Feng Cao (Liaoning University of Technology), Hao Sun1
Estimated H-index: 1
(Liaoning University of Technology)
+ 1 AuthorsShaoceng Tong64
Estimated H-index: 64
(Liaoning University of Technology)
This paper investigates the fuzzy adaptive fault-tolerant control design problem for a class of electromagnetic active suspension systems. The change of the contact between the tire and the ground is studied to increase the vehicle stability in the presence parameter uncertainties. Meanwhile, considering the nonlinearity of the spring in the suspension space, the characteristics of the damper are studied to form the basis of accurate control. Furthermore, unknown time-varying delay and dynamic a...
Published on Sep 1, 2019in Fuzzy Sets and Systems2.91
Jianrong Zhao (Nanjing University of Science and Technology), ShengyuanXU69
Estimated H-index: 69
(Nanjing University of Science and Technology),
Ju H. Park60
Estimated H-index: 60
(Yeungnam University)
Abstract This paper studies a problem of the sampled-data stabilization for Takagi-Sugeno fuzzy systems with actuator failures. An improved Lyapunov functional is constructed, which is dependent on the fuzzy membership functions FMFs and includes the sampling states with two sampling instants. A new integral term including the FMFs is introduced into this Lyapunov functional for the first time. Each term in this Lyapunov functional need not be positive, but it should be positive at sampling inst...
Jun-Wei Wang13
Estimated H-index: 13
(USTB: University of Science and Technology Beijing)
The problem of dynamic boundary fuzzy control design is investigated in this paper for nonlinear parabolic partial differential equation (PDE) systems with spatially noncollocated discrete observation. Two cases of noncollocated discrete observation in space (i.e., pointwise observation in space and local piecewise uniform observation in space) are considered, respectively. The spatially noncollocated discrete observation makes the control design very difficult. Such design difficulty can be sur...
Wen-Bo Xie (Harbin University of Science and Technology), Tong-Zhi Wang (Harbin University of Science and Technology)+ 1 AuthorsYulong Wang1
Estimated H-index: 1
(SHU: Shanghai University)
Abstract For continuous-time nonlinear systems represented by Takagi–Sugeno fuzzy models, a new H ∞ reduced-order-observer based controller synthesis structure is investigated in this paper. By the fuzzy reduced-order observer and fuzzy controller, an augmented error system composed of the estimation and control errors is obtained. The fuzzy modeling residual terms are seen as part of the external disturbance, and an extra design matrix is added to facilitate the design process. The robustness a...
Published on Jul 1, 2019in Neurocomputing4.07
Meng Han (Yanshan University), Hak-Keung Lam43
Estimated H-index: 43
('KCL': King's College London)
+ 2 AuthorsChangzhu Zhang (Tongji University)
Abstract This paper presents a methodology to investigate the observer-based control for positive nonlinear systems with unknown time delay through analyzing the stability and positivity of positive polynomial fuzzy-model-based (PPFMB) observer-control systems with unknown time delay and unmeasurable premise variables. In order to widen the application of research results and relax the research results, the polynomial fuzzy observer-controller employs a membership function depending on estimated...
Published on Jan 1, 2018in IEEE Transactions on Fuzzy Systems8.76
Xin Wang7
Estimated H-index: 7
(University of Electronic Science and Technology of China),
Xin Wang2
Estimated H-index: 2
+ 2 AuthorsLin Shi2
Estimated H-index: 2
This paper studies the problems of stability and stabilization of a class of chaotic systems (CSs) with Takagi–Sugeno fuzzy model and nonuniform sampling. It designs a fuzzy sampled-data protocol based on a switched idea to tackle the stability issue of such systems. Novel criteria on stabilization of CSs are established by employing a fuzzy membership function (FMF)-dependent Lyapunov functional and the information of the time derivative of FMFs, which significantly utilize the available charac...
Published on Mar 1, 2019in Neurocomputing4.07
Xiao-Lei Wang1
Estimated H-index: 1
(NU: Northeastern University),
Guang-Hong Yang52
Estimated H-index: 52
(NU: Northeastern University)
Abstract This paper is concerned with the problem of fault detection (FD) for T-S fuzzy systems with measurement outliers. A new fuzzy FD observer with adaptive saturation of output errors is first constructed to reduce the effect of measurement outliers on the error systems and the residual signals. Then, by establishing a suitable non-differentiable Lyapunov function, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure the exponential stability and H ∞ per...
Published on Jan 1, 2018in IEEE Access4.10
Rathinasamy Sakthivel3
Estimated H-index: 3
(Bharathiar University),
S. Harshavarthini (Bharathiar University)+ 1 AuthorsYong-Ki Ma5
Estimated H-index: 5
(KNU: Kongju National University)
In this paper, the robust trajectory tracking controller is proposed for a class of Takagi–Sugeno fuzzy Markovian jump time-varying delay systems with unknown uncertainties and disturbances. Precisely, uncertainty and disturbance estimation-based control design is developed for the addressed systems under uncertain environment. By exploiting the Lyapunov technique and Wirtinger-based integral inequalities, a sufficient condition is derived for ensuring the robust trajectory tracking performance....
View next paperOn stability analysis of fuzzy systems with interval time-varying delay