Stability Analysis of T–S Fuzzy Control System With Sampled-Dropouts Based on Time-Varying Lyapunov Function Method

Wang, Zhanshan; Sun, Jian; Zhang, Huaguang

doi:10.1109/tsmc.2018.2822482

Cited by 40 publications

(16 citation statements)

References 34 publications

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“…Lemma 1 has verified that although all the Lyapunov functions are exponentially divergent, one can derive the ‘decline’ characteristic at switching instants to achieve the overall convergence. It has overcome the traditional ‘jump’ phenomenon at switching instants for multiple Lyapunov functions [19, 29]. But in this study, it is difficult to derive condition (12) at all the switching instants

T_{r}

since there exist discrete signals generated by event‐triggered control and such discrete signals are not measurable with time.…”

Section: Resultsmentioning

confidence: 99%

Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Sun

Wang

Fan

2020

IET Control Theory & Appl

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The consensus problem for a class of multi-agent systems with switching jointly connected topologies via periodic event-triggered control is studied. The distinguishing feature of such system is that the eigenvalues of system matrix can contain positive real parts. Due to the coexistence of unstable system matrix and disconnected topologies, the agents can diverge from each other across some periods even if the control input is imposed on them. To overcome this difficulty, a periodic-sampling time unit (PSTU) approach is introduced to analyse the local convergence or divergence property within each sampling time unit based on the periodic event-triggering control. Then the stabilisation property of switching behaviours is utilised to compensate the divergence within each switching interval via the dwell time technique. It is interesting to see that each switching period is considered to consist of finite number of PSTUs. Then by confining a pair of lower and upper bounds on the dwell time, the overall consensus can be reached. Further, a novel class of event-dependent discretised Lyapunov functions are utilised to describe the error characteristics and computable conditions for the overall consensus can be derived. Finally, the effectiveness of the proposed result is illustrated by a numerical example.

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T_{r}

since there exist discrete signals generated by event‐triggered control and such discrete signals are not measurable with time.…”

Section: Resultsmentioning

confidence: 99%

Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Sun

Wang

Fan

2020

IET Control Theory & Appl

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“…After converting into a class of T–S fuzzy models, the analysis and synthesis of the nonlinear systems become easy and the conventional linear system theories could be utilized. Moreover, many achievements have been made in the research of T–S fuzzy systems, for instance References 8‐14. A stabilization issue for the discrete‐time nonlinear system against external disturbance, multiplicative noises, and multiple constraints was researched in accordance with the definition of Lyapunov stability in Reference 8.…”

Section: Introductionmentioning

confidence: 99%

Robust reliableH_∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay

Sun

Zhang

et al. 2021

Optim Control Appl Methods

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In this article, the problems of robust reliable H∞ optimization control for discrete‐time nonlinear systems with or without time‐delay subject to faults are investigated. A static state feedback controller is explored for Takagi–Sugeno fuzzy systems against nonlinear dynamics, exogenous disturbances, and model uncertainties. In contrast to the design of conventional controllers, the proposed controller is easier and more flexible. The Lyapunov function is utilized to assure the stability of the closed‐loop systems. Besides, linear matrix inequalities are utilized to derive the sufficient conditions by MATLAB toolbox. Finally, two simulation examples are shown to validate the feasibility of the suggested approach.

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“…The designing of controller and stability analysis can be deduced in the context of linear matrix inequalities (LMIs) for T‐S fuzzy model and the parallel distributed compensation (PDC) suggests a strategy to design a fuzzy controller based on the provided T‐S fuzzy model 47 . In Reference 48, the stability issue of T‐S fuzzy control systems are investigated by considering time varying Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

Observer‐based controller design for uncertain disturbed Takagi‐Sugeno fuzzy systems: A fuzzy wavelet neural network approach

Ebrahimi

Asemani

Safavi

2020

Adaptive Control & Signal

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SummaryIn this article, we develop a novel method to design a controller for nonlinear systems represented by Takagi‐Sugeno (T‐S) fuzzy model in the presence of unknown dynamics, uncertainties in parameters of nonlinear system and external disturbances. The control law is constituted two segments. The first segment derives from parallel distributed compensation (PDC) procedure, in which each control rule is drawn from the respective rule of T‐S fuzzy model. The second segment stems from fuzzy wavelet neural network (FWNN) estimator which is evoked by the hypothesis of multiresolution analysis (MRA) of wavelet transforms and fuzzy notions, so as to approximate the uncertainties and external disturbances in T‐S fuzzy model accurately. In this regard, the Lyapunov stability theorem is applied to acquire the adaptive learning laws for training and tuning online FWNN parameters such as the dilations, translations, and the weights of networks. Moreover, the asymptotic stability of the closed loop system is guaranteed based on the Lyapunov stability theorem. Furthermore, a development of the proposed method to observer‐based controller design for uncertain nonlinear systems descripted by T‐S fuzzy model is provided. The efficiency and robustness of the proposed method are illustrated by simulation outcomes. It is noteworthy that the proposed controller remarkably handles the uncertainties and external disturbances in T‐S fuzzy model without employing traditional conservative lemma and without considering bounds on uncertainties.

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Stability Analysis of T–S Fuzzy Control System With Sampled-Dropouts Based on Time-Varying Lyapunov Function Method

Cited by 40 publications

References 34 publications

Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Robust reliableH_∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay

Observer‐based controller design for uncertain disturbed Takagi‐Sugeno fuzzy systems: A fuzzy wavelet neural network approach

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Stability Analysis of T–S Fuzzy Control System With Sampled-Dropouts Based on Time-Varying Lyapunov Function Method

Cited by 40 publications

References 34 publications

Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Robust reliableH∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay

Observer‐based controller design for uncertain disturbed Takagi‐Sugeno fuzzy systems: A fuzzy wavelet neural network approach

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Robust reliableH_∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay