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Summary: This manuscript concerns the stabilization of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with additive time‐varying delay components. By constructing a suitable fuzzy Lyapunov‐Krasovskii functional (LKF) with membership functions, the sufficient condition of the stability criteria has been established for the discrete‐time T‐S fuzzy systems with additive time‐varying delays. To do this, the extended version of Wirtinger's inequality is used to bound the forward differences of the LKF. By utilizing the T‐S fuzzy model approach, the dynamics of each fuzzy rule is expressioned by a linear system. Then, a fuzzy controller is designed to guarantee the H∞$$ {H}_{\infty } $$ performance of the closed‐loop system formulated in terms of linear matrix inequalities (LMIs). Finally, the numerical simulations are carried out to demonstrate the effectiveness and feasibility of our theoretical findings. [ABSTRACT FROM AUTHOR]

This study concerns the stabilization criteria of Takagi–Sugeno (T–S) fuzzy systems under the memory-based sampled-data control. Contrasted to the traditional sampled-data control strategy, a more general control scheme that admits the signal transmission delay and the multiplicative control gain uncertainties is designed. In order to indicate the perturbations of control gain, the Bernoulli sequence is applied to the designed control scheme. At the same time, the membership function dependent $H_{\infty }$ performance index is introduced to attenuate the disturbances of continuous-time T–S fuzzy systems for the first time. By utilizing the novel $H_{\infty }$ performance index together with the appropriate Lyapunov–Krasovskii functional, including the information of sampling period and signal transmission delay, the sufficient conditions are derived in the framework of linear matrix inequalities. These conditions ensure the stabilization of concerned T–S fuzzy systems and enlarging the maximum sampling period. At last, the advantages of the derived results are shown by the numerical examples. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability analysis for the fuzzy-based sampled-data control (SDC) systems, which is based on a fractional parameter-based refined looped-Lyapunov functional (RLLF). To do this, with the help of the Takagi–Sugeno fuzzy method, a SDC can be designed. To derive sufficient criteria, a RLLF with information about the sampling period is proposed. In the RLLF, a fractional parameter is introduced and it has more information on the splitted sampling intervals and delayed states with a fractional parameter. The derived criteria guarantee the asymptotic stability of the proposed system with a $H_{\infty }$ attenuation level. To validate the derived conditions, a state-space model of nonlinear permanent magnet synchronous motor is proposed. Besides, comparison examples are conducted for analyzing the less conservatism of the merit of the proposed methods. Finally, the simulation outcomes are illustrated the superiority of the work. [ABSTRACT FROM AUTHOR]

This article investigates the stabilization problem of the Takagi–Sugeno (T–S) fuzzy-based interval type-2 (IT-2) reliable sampled-data control system. Different from the existing studies, the information for the entire sampling interval with a relation of the augmented state vectors is considered for designing the reliable sampled-data control of IT-2 T–S fuzzy systems. In this regard, we construct the suitable looped Lyapunov–Krasovskii functional (LKF) with the information of the fuzzy membership function that feeds back the time derivative of the membership function to derive sufficient conditions. These sufficient conditions are established in the form of linear matrix inequalities (LMIs), which ensure the global asymptotic stability of T–S fuzzy systems under the designed control technique. Finally, the applicability and superiority of developed reliable sampled-data control techniques were validated by three practical systems. [ABSTRACT FROM AUTHOR]

This article concerns the problem of stability analysis of nonlinear systems under the sampled-data control (SDC) with actuator faults. The addressed nonlinear systems can be expressed by a number of linear arrangements, based on the Takagi–Sugeno (T–S) fuzzy technique. The time-dependent SDC with actuator faults of the addressed nonlinear systems delineates based on the input model of Markovian variability. The time-scheduled Lyapunov functional and the looped-functional are taken together in the production of a Lyapunov functional candidate. Based on a free matrix-based integral inequality and the Lyapunov functional, some sufficient linear matrix inequality conditions are delivered to guarantee the mean-square asymptotic stability under $H_\infty$ performance of the considered sampled-data T–S fuzzy systems with actuator faults. Finally, we demonstrate the feasibility and strength of our proposed method through some examples. [ABSTRACT FROM AUTHOR]

In this article, the disturbance observer (DOB)-based memory integral sliding-mode control (ISMC) is designed for the permanent magnet synchronous motor (PMSM) model subject to mismatched disturbance through the Takagi–Sugeno (T–S) fuzzy approach. Different from the previous studies, a memory-based ISMC scheme that has a constant delay is taken for the first time to design the ISMC for the T–S fuzzy systems. The DOB is given to estimate the disturbances, which are incorporated in the controller design to counteract the disturbance. To fully abide by the model characteristics of the PMSM-based T–S fuzzy systems and DOB, an integral-type fuzzy switching surface function (IFSSF), which involves state-dependent input matrix and memory parameter simultaneously, is defined. From the IFSSF, the fuzzy ISMC is designed to ensure the reachability condition in finite time. Besides that, the designed fuzzy ISMC can effectively attenuate the mismatched disturbances based on the $H_{\infty }$ control theory. Also, a set of sufficient conditions is derived to ensure the global asymptotic stability for the sliding-mode dynamics by the proposed controller. Finally, the applicability of designed DOB-based memory fuzzy ISMC methodology is demonstrated by a controller design for the PMSM model. [ABSTRACT FROM AUTHOR]

This study isrelevant to the topic of a robust event‐triggered mechanism for the Takagi–Sugeno (T–S) fuzzy system with successive time‐delay (STD) signals and its application, where the uncertainties satisfy the randomly occurring form. Firstly, an event‐triggered communication scheme is introduced, which can adaptively adjust the communication threshold to save limited communication resource. The primary aim of this study is to model an event‐triggered mechanism with STD, which ensures that the suggested T–S fuzzy system achieves extended dissipative with permissible uncertainties. Secondly, by using the relaxed integral inequality technique, single and double auxillary function‐based integral inequalities to evaluate the derivative of the designed Lyapunov–Krasovskii functional, quadratically stable condition is established for the delayed fuzzy system in terms of linear matrix inequalities and analyse the H∞,L2−L∞, passivity, mixed H∞ and passivity, (Q,S,R)‐dissipativity execution by choosing the weighting matrices can be solved simultaneously in a standard framework based on the idea of extended dissipative. Finally, simulation studies are given to verify the effectiveness of the derived results, among them one example was supported by the real‐life application of the benchmark problem in the sense of STD signals. [ABSTRACT FROM AUTHOR]

This article investigates the nonfragile retarded fuzzy sampled-data control design of Takagi–Sugeno (T–S) fuzzy system. When compared to the traditional sampled-data control scheme, a constant signal transmission delay is involved with uncertainties in control gain parameters, which exploited for the first time to tackle the stabilization analysis of the closed-loop T–S fuzzy systems based on the switched control idea. By constructing a fuzzy membership function (FMF)-dependent Lyapunov–Krasovskii functional (LKF) and utilizing the time-derivative information of the FMF, the sufficient conditions are carried out in terms of linear matrix inequalities (LMIs) such that the resultant T–S fuzzy systems can achieve the globally asymptotically stable under the designed control. Then, the desired control gain is determined by solving the obtained LMIs. Finally, the numerical simulations are demonstrated to show the advantage and applicability of the derived sufficient conditions. [ABSTRACT FROM AUTHOR]

This study addresses the finite‐time non‐fragile sampled‐data control for a Takagi–Sugeno (T–S) fuzzy system with passivity and passification approaches. Firstly, a new finite‐time boundedness (FTB) condition is acquired for the considered system by using a Lyapunov–Krasovskii functional and inequality approaches. Secondly, finite‐time passivity (FTP) conditions are achieved to ensure that the T–S fuzzy system is not only FTB but also finding passivity performance index. Moreover, under the FTP conditions, the non‐fragile sampled‐data controller is designed for linear matrix inequalities to achieve the stability conditions of the considered system. Finally, the corresponding simulation results for the application examples related to a permanent magnet synchronous motor system, truck trailer system, and Lorenz system are applied to verify the performance of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, sampled-data control is proposed to stabilize the nonlinear system, which is expressed as a Takagi–Sugeno (T–S) fuzzy submodels. Based on suitable Lyapunov– Krasovskii functional (LKF) along with new weighted integral inequalities, the sufficient conditions are derived in terms of linear matrix inequalities, which ensure the exponential stability of the proposed closed loop T–S fuzzy system. The peculiarity of this paper is: as novel integral inequalities and LKF are proposed, less conservative results are provided when compared to existing results. Besides that, wind energy conversion systems, chaotic systems, and an inverted pendulum are validated with derived sufficient conditions. The corresponding simulation results show the merit of the proposed results over the existing works. [ABSTRACT FROM AUTHOR]

The present study mainly focuses on designing a stochastic sampled‐data controller for chaotic Takagi–Sugeno (T–S) fuzzy systems. Distinct to the existing controller schemes, in this work, the random time delay is introduced into the proposed control scheme that ensures the exponential stabilisation of T–S fuzzy models. In addition, the input delays are assumed to be randomly time‐varying, which copes with the traditional uncorrelated Bernoulli distributed sequences. Based on the proposed Lyapunov–Krasovskii functional and using new weighted integral inequalities, the stability and stabilisation conditions are derived and expressed in terms of linear matrix inequalities, which ensure the exponential stability of the states. Finally, in the simulation results, the chaotic nature of two dynamical systems are considered for validation of the derived conditions. From the simulation results, it is concluded that the proposed method can provide better stability performance and less conservative results. [ABSTRACT FROM AUTHOR]

In this study, an event‐triggered fuzzy controller is designed to stabilise a class of non‐linear systems expressed as a Takagi–Sugeno (T–S) fuzzy model with mismatched membership functions. At first, an event‐triggered fuzzy controller has been designed in terms of induced time delay. Secondly, the event‐triggered fuzzy system is presented as a time‐delay model with the asynchronous premise variables. Then, by introducing a time‐dependent Lyapunov–Krasovskii functional and based on the fuzzy based control approach, linear matrix inequality‐based stability conditions are established to guarantee the asymptotic stability of the proposed T–S fuzzy model. The derived conditions utilise the information on the membership functions of both fuzzy system and fuzzy controller. Finally, the proposed theoretical results are applied to stabilise the variable speed wind turbine system while saving the limited network resources. Further, through the truck–trailer example, the merits and the design procedure of the proposed technique have been demonstrated. [ABSTRACT FROM AUTHOR]

This study proposes an intelligent digital redesign (IDR) technique for sampled‐data fuzzy filters of non‐linear systems. The technique constructs a closed‐loop system with predesigned continuous‐time and sampled‐data filters based on the Takagi–Sugeno (T–S) fuzzy model. The closed‐loop systems ensure asymptotic stability and state‐matching condition in the IDR problem. Unlike previous techniques, the proposed method solves the IDR problem without a discretization process which degrades the IDR performance. Sufficient conditions for solving the IDR problem are proposed and derived in terms of linear matrix inequalities. In addition, the performance recovery of the sampled‐data fuzzy filter is shown. Finally, the feasibility of the proposed technique is demonstrated in two simulation examples. [ABSTRACT FROM AUTHOR]

This paper presents an output-feedback exponential stabilization condition of sampled-data polynomial fuzzy control systems under variable sampling rates. Compared with previous work, the proposed method is less conservative because of the newly developed time-dependent fuzzy Lyapunov–Krasovskii functional that is based on the conventional fuzzy Lyapunov function. Moreover, the controller is allowed to contain polynomial gain matrices, thereby improving the control performance and design flexibility. This is realized by assuming the difference between the continuous- and discrete-time state vectors as time-varying norm-bounded uncertainties, which are manipulated using a robust control technique. A new sufficient condition is introduced to cast the stability condition containing the integral term as the sum-of-square conditions. Finally, the effectiveness of the proposed method is validated by simulations. [ABSTRACT FROM PUBLISHER]

This study presents a linear matrix inequality (LMI) approach to the sampled‐data control of Takagi–Sugeno fuzzy systems, based on the intelligent digital redesign (IDR) technique. The objective of the IDR is to design a digital control system whose trajectory closely matches that of a given well‐constructed analogue control system by minimising the state‐matching error. In this study, state‐matching performance is enhanced by using a continuous‐time state‐matching criterion, which guarantees that the state‐matching error is minimised through the entire time interval. Unlike previous studies, mismatched information of membership functions for both analogue and digital control systems is directly manipulated. Moreover, the authors introduce an improved fuzzy Lyapunov functional that consists of both membership functions for analogue and digital control systems, which relaxes the conservativeness of LMI conditions. Finally, two examples demonstrating the effectiveness of the authors' method are provided. [ABSTRACT FROM AUTHOR]

• In this study, time-delay, nonlinear perturbation, and external disturbance are taken into account and expressed as a delayed T-S FS. Then, H ∞ -based DDS conditions are derived under the fuzzy ISMC scheme. • Different from the existing SMC, a fuzzy integral sliding surface is constructed with delayed states. Moreover, RBF NNs are utilized to approximate the nonlinearity of the proposed TS FM. Based on this, an adaptive RBF NNs-based fuzzy ISMC is designed for maintaining the state trajectories on the sliding surface from the initial time instant. • The DDS conditions are derived by using suitable L-F with an augmented functional, and the generalized free-weighting-matrix (GFWM)-based lemma is used to estimate the integral parts in V ˙ (t). • The enhancement of the result is highlighted by comparing the proposed result with the existing results [12–16] and producing better results than them. This paper presents a method for designing adaptive neural networks (NNs) based on integral sliding mode control (ISMC) for delayed Takagi-Sugeno fuzzy systems with external disturbances. To do this, a fuzzy sliding surface is constructed with the information of the delayed states, and an adaptive radial basis function (RBF) NNs-based fuzzy ISMC is designed. Here, the RBF NN function is utilized to approximate the nonlinear perturbation term. The resulting stability criteria are derived based on suitable Lyapunov functionals with the help of generalized free-weight matrix-based inequality. The resulting conditions ensure the asymptotic stability with H ∞ attenuation level. Moreover, the designed sliding motion achieved the reachability condition under the adaptive RBF NNs based on the sliding mode controller. To end with, a design and comparative examples are given to show the success of the nominated control scheme and less conservatism of the derived sufficient conditions. [ABSTRACT FROM AUTHOR]

This paper addresses the novel stabilization criteria for a nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS) with sampled-data information, subject to the uncertainty and controller gain variations. In this regard, the nonlinearity in PMSG-based WTS is conferred by the Takagi–Sugeno (T–S) fuzzy systems. Next, by employing the full advantages of the variable characteristic related to the sampling pattern, a novel looped-type asymmetric augmented Lyapunov-Krasovskii functional (LKF) is developed. Then, the dynamic delay partition method is the first time to be applied for the non-fragile sampled-data control design of proposed T–S fuzzy systems. Also, the less conservativeness stabilization criteria for T–S fuzzy systems are obtained in the form of linear matrix inequality. In the end, the numerical examples confirm the applicability and efficiency of the presented results. • The nonlinear PMSG-based WTS is modeled with an uncertainty of stator resistance. • The non-fragile SDC is designed for T–S fuzzy-based PMSG WTS. • By utilizing the delay partition method, the novel looped LKF is constructed. • A matrix Q in proposed LKF are all not required to be symmetric or positive definite. • The numerical examples assure the applicability and superiority of presented results. [ABSTRACT FROM AUTHOR]

In this paper, local stability and local stabilization problems are considered for discrete-time nonlinear systems represented by Takagi–Sugeno (T–S) fuzzy systems. Improved methods to assess the local stability, design locally stabilizing control laws, and estimate the domain of attraction are developed in terms of single-parameter minimization problems subject to linear matrix inequality (LMI) constraints. The improvement is achieved by applying a convergent LMI relaxation technique to prove positivity of homogeneous polynomial parameter-dependent matrices of arbitrary degree with variables in the simplex. We also take advantage of the recently developed parameter variation modeling technique to deal with the case that the variation rate of the membership functions of the T–S fuzzy systems is bounded and less than one. Finally, several illustrative examples demonstrate the validity and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This study deals with the problem of local stability analysis and the computation of invariant subsets of the domain of attraction (DA) for discrete‐time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions, new sufficient conditions and an iterative scheme are proposed in order to prove the local stability and to estimate the DA. The mean value theorem and polytopic type bounds on the gradient of the membership functions are used to consider the relation between the membership functions at samples k and k + 1. Each step of the iterative procedure consists of linear matrix inequalities (LMIs) or single‐parameter minimisation problems subject to LMI constraints, which are solvable via convex optimisations. Finally, examples compare the proposed conditions with existing tests. [ABSTRACT FROM AUTHOR]

In this study, the nonparallel distribution compensation (PDC) control is proposed for permanent magnet synchronous generator (PMSG)-based wind energy conversion systems (WECS). To do this, the nonlinear PMSG-based WECS is expressed by Takagi-Sugeno (T-S) fuzzy systems. Based on the imperfect premise matching, the T-S fuzzy observer is delineated for estimating the unmeasurable states of the proposed WECS. Unlike the traditional PDC control, a general non-PDC control strategy is designed via the T-S fuzzy observer. The designed control scheme indicates that it is not required to share the same membership functions as the observer and system. By constructing the Lyapunov functional with available information on the fuzzy membership function and introducing the slack variables, sufficient conditions are obtained to assure the asymptotic stability of error dynamic for the PMSG-based T-S fuzzy system and its observer. Finally, the feasibility and applicability of the derived theoretical results are validated through the numerical example. [ABSTRACT FROM AUTHOR]

This paper presents a new fuzzy Lyapunov function (FLF) for the stability analysis of continuous-time Takagi–Sugeno (T–S) fuzzy systems. Unlike conventional FLFs, the proposed one depends not only on the fuzzy weighting functions of the T–S fuzzy systems but on their first-order time derivatives as well. Based on the proposed FLF, a sufficient stability condition is derived in the form of linear matrix inequalities, depending on the upper bounds on the second-order time derivative of the fuzzy weighting functions, as well as the first-order ones. Finally, some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a simple and systematic control design method is proposed for making a continuous-time Takagi–Sugeno (T–S) fuzzy system chaotic. The concept of parallel distributed compensation is employed to determine the structure of a fuzzy controller from a T–S fuzzy model. The fuzzy controller makes the T–S fuzzy model, which could be stable or unstable, bounded and chaotic. The verification of chaos in the closed-loop T–S fuzzy system is done by the following procedure. First, we establish an asymptotically approximate relationship between a continuous-time T–S fuzzy system with time-delay and a discrete-time T–S fuzzy system. Then, we verify the chaos in the closed-loop T–S fuzzy system by applying the Marotto theorem to its associated discrete-time T–S fuzzy system. The generated chaos is in the sense of Li and Yorke. Two examples are given to show that this methodology is simple and effective for anticontrol of chaos for a continuous-time T–S fuzzy system. [ABSTRACT FROM AUTHOR]

An approach is proposed for making chaotic a given stable Takagi-Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable TS fuzzy system, where the chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design. [ABSTRACT FROM AUTHOR]

The paper is concerned with the development of a sampled-data (SD) controller designed for Takagi–Sugeno (T–S) fuzzy systems. A key highlight is the incorporation of a refined fractional delayed-state into this control approach. The primary aim is to establish criteria for system stabilization, thereby ensuring the asymptotic stability of the considered systems. This objective is pursued within the framework of the newly designed control methodology. The core contribution of work explains in the introduction of an innovative Lyapunov–Krasovskii functional (LKF) tailored to T–S fuzzy systems. This novel approach capitalizes on the efficacy of sampling intervals. The LKF design takes advantage of variable attributes tied to the real sampling pattern, effectively reducing the conservatism of the outcomes. Moreover, the paper introduces a sophisticated fractional delayed-state concept, which plays a pivotal role in shaping a modified looped functional-based LKF. The stability criteria are then formulated through the utilization of linear matrix inequalities (LMIs) and integral inequalities. These criteria perform dynamic part in establishing the asymptotic stability of considered systems when subjected to the designed control approach. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology of robust state feedback fuzzy controller based on free weighting matrix method for a class of uncertain Markovian jump nonlinear systems. The class of systems under consideration is represented by the T–S fuzzy model with partly known transition probability matrix. The free weighting matrix method is proposed to obtain a less conservative stochastic stability criterion of the uncertain Markovian jump fuzzy systems (MJFSs) in terms of linear matrix inequalities (LMIs). Furthermore, a sufficient condition for the mode-dependent state feedback fuzzy controller is derived for the MJFSs for all admissible parameter uncertainties. Finally, a simulation example is provided to illustrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new stabilization condition for discrete-time Takagi–Sugeno (T–S) fuzzy systems. To this end, the previously developed periodic nonparallel distributed compensation (non-PDC) control law is extended to the more general one whose gain matrix has a block lower triangular matrix form. A distinguished feature of the proposed control law is that it uses a discrete-time feedback loop incorporating information from the previous states of the system. The resultant stabilization condition is represented in the form of linear matrix inequalities (LMIs). In addition, we show that the proposed condition includes the existing one based on the periodic control approach as a particular case. Finally, examples are given to show that the proposed condition provides less conservative results than those of the existing ones published in the literature. [Copyright &y& Elsevier]

Abstract: This paper provides simple and effective linear matrix inequality (LMI) characterizations for the stability and stabilization conditions of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To do this, more general classes of non-parallel distributed compensation (non-PDC) control laws and non-quadratic Lyapunov functions are presented. Unlike the conventional non-quadratic approaches using only current-time normalized fuzzy weighting functions, we consider not only the current-time fuzzy weighting functions but also the -step-past () and one-step-ahead ones when constructing the control laws and Lyapunov functions. Consequently, by introducing additional decision variables, it can be shown that the proposed conditions include the existing ones found in the literature as particular cases. Examples are given to demonstrate the effectiveness of the approaches. [Copyright &y& Elsevier]

This study concerns the exponential stability and stabilization problem for the Takagi–Sugeno (T–S) fuzzy systems under the membership function dependent (MFD) H∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$_\infty $$\end{document}-based sampled-data control (SDC) using an improved exponential two-sided looped-functional (TSLF) approach. First, an exponential TSLF is introduced to achieve the state information within the intervals tk\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$t_{\textrm{k}}$$\end{document} to t and t to tk+1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$t_{\textrm{k}+1}$$\end{document}, which not only relaxes the monotonic constraint but would also not impose the terms as positive definite. By employing the concept of looped-functional, a new exponential TSLF is introducing the exponents e2α(t-tk),\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$e^{2\alpha (t-t_{\textrm{k}})},$$\end{document}e2α(tk+1-t)-12α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\frac{e^{2\alpha (t_{\textrm{k}+1}-t)}-1}{2\alpha }$$\end{document}, and e-2α(t-tk)-12α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\frac{e^{-2\alpha (t-t_{\textrm{k}})}-1}{2\alpha }$$\end{document}, thereby enhancing the control performance, design flexibility and also it contains the more actual sampling information of system states. Next, the new exponentially stable lemma is derived from the fuzzy SDC system with an external disturbance. To this end, the time derivatives of exponential TSLF-based Lyapunov–Krasovskii functional, some stabilization criteria exist in formulating linear matrix inequalities to secure the system is exponentially stable under MFD H∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$_\infty $$\end{document} criterion. Finally, the chaotic permanent magnet synchronous generator-based wind energy system is demonstrated under the practical values with proposed sufficient conditions, and Rossler’s model expresses the advantages and excellence of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper presents a decentralized sampled-data H ∞ fuzzy filter design method for nonlinear large-scale systems which are represented by a Takagi–Sugeno (T–S) fuzzy model. Based on the T–S fuzzy model, the error system between the nonlinear large-scale system and the filter is obtained. The discretization process of the error system is accomplished with the exact discrete-time approach to eliminate the exact-approximate mismatch. By using the discrete-time Lyapunov sense, the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the H ∞ norm is ensured to guarantee the H ∞ fuzzy filter performance. Finally, numerical examples are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]