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This study focuses on examining the issues of extended dissipative-based composite anti-disturbance reliable tracking control for stochastic Takagi–Sugeno fuzzy systems afflicted by sensor faults and multiple disturbances. Explicitly, the multiple disturbances include the autonomous Wiener process and non random noises with partly known information that are generated by an exogenous plant. To address the difficulty of estimating the non random disturbance while considering the partially known information, the study incorporates a fuzzy stochastic disturbance observer. Furthermore, to solve the output tracking issue of the system under consideration, a modified repetitive tracking control is implemented. Then, combining the methodologies of disturbance observer-based control technique with modified repetitive control, a composite anti-disturbance reliable tracking control strategy is developed for achieving the intended tracking goal despite the multiple disturbances and sensor faults encountered. Additionally, the proposed approach involves extended dissipativity scheme, which includes $ H_\infty $ H∞, passivity, dissipativity, and $ \mathfrak {L}_2 - \mathfrak {L}_\infty $ L2−L∞ performances in a unified framework. In particular, by employing Lyapunov–Krasovskii functional approach, the essential stability criteria for the proposed closed-loop system are articulated in the form of linear matrix inequalities. Additionally, numerical illustrations are presented to exemplify the application and efficiency of the developed control protocol. [ABSTRACT FROM AUTHOR]

This research endeavour's primary attention is on the problems of stabilization and multiple disturbance rejection for a class of interval type-2 fuzzy stochastic systems that are prone to parameter uncertainties and multiple disturbances. Specifically, the multiple disturbances are classified into two aspects: the first aspect is matched disturbances, which emanate from an exogenous system, while the second aspect is norm-bounded mismatched disturbances. Further, to provide a precise estimation of the matched disturbances, a fuzzy rule-based multiple disturbance observer is built. Based on the estimated information from the framed observer, a disturbance estimation-based resilient control is devised that can withstand the effects of disturbances. Besides, the footprints of mismatched kind of disturbances are handled by employing the $ (\mathcal {Q},\mathcal {S},\mathcal {R})-\tilde \varsigma $ (Q , S , R) − ς ~ dissipative performance. Moreover, to insure the attainment of the foremost objective of this analysis, a collection of suitable criteria has been developed by means of linear matrix inequalities with the satisfied disturbance attenuation index through Lyapunov's theory of stability. In addition, under the lighting of adequate conditions, the gain matrices of the configured controller and the framed observer can be determined. Finally, two simulation examples are supplied as a conclusion to the examination, each serving to illustrate the potency and viability of the designed control scheme and the presented theoretical findings. [ABSTRACT FROM AUTHOR]

Summary: With the aid of a proportional integral framework, the presented article focuses on the problems of finite‐time boundedness and fault estimation for Takagi–Sugeno fuzzy singular systems subject to time delays, faults and external disturbances. To commence, we conjure up a fuzzy‐dependent intermediate variable and from thereon, a proportional integral‐based fuzzy intermediate estimator is constructed. Moreover, the constructed estimator precisely facilitates for estimating the fault signals and system states in simultaneously. Besides this, the integral term in the proportional integral estimator offers greater design flexibility and higher resilience. Secondly, an intermediate estimator‐based fault‐tolerant control is devised by availing the information from the proportional integral‐based fuzzy intermediate estimator, which aids in effectively compensating the faults arising in the system. Subsequently, by setting up an appropriate Lyapunov–Krasovskii functional, the set of adequate requirements asserting the finite‐time boundedness with the endorsed mixed H∞$$ {H}_{\infty } $$ and passivity performance index is established in terms of linear matrix inequalities. After that, an explicit framework for the requisite gain matrices can be found forth basing on the formed linear matrix inequality criteria. Ultimately, simulation findings are supplied to evaluate the utility and applicability of the theoretical insights. [ABSTRACT FROM AUTHOR]

This research addresses the problems of finite-time boundedness and disturbance rejection for T-S fuzzy networked systems that are vulnerable to actuator faults, linear fractional uncertainties and multiple disturbances through a reliable anti-disturbance control design. In particular, multiple disturbances encompasses two kinds, where the first kind of disturbance is matched, which is produced by fuzzy exogenous systems and the second kind is mismatched disturbance, which is norm-bounded. Moreover, in order to depict the reality more precisely, the actuator faults are taken into account in the system under consideration. In particular, the fuzzy disturbance observer is constructed for closely estimating the matched disturbances. After that, a reliable anti-disturbance controller is designed in accordance with the output of the conceived disturbance observer. Furthermore, the (ξ 1 , ξ 2 , ξ 3) - η dissipative performance is deployed in order to reduce the imprints of mismatched disturbances to the greatest extent feasible. Moreover, by constructing a Lyapunov-Krasovskii functional, a set of adequate criteria in the form of linear matrix inequalities is established, which guarantees that the undertaken system achieves finite-time boundedness. In conclusion, two numerical examples are shown, one of which is a model of a tunnel diode circuit, which reveals the competence and applicability of the suggested control mechanism. [ABSTRACT FROM AUTHOR]

The issues of input–output finite-time stability and stabilization of Takagi–Sugeno (T–S) fuzzy systems with time-varying state delay and exogenous input signal are studied in this article. For the stabilization process, a controller that does not share the same membership functions as the system is considered and the state feedback is quantized by using a logarithmic quantizer. The desired stability criterion for the addressed fuzzy system is first derived without the control term. It is then extended to the case in which the proposed controller is present. The stability criteria are given in the form of matrix inequalities, which are supported by the augmented Lyapunov–Krasovskii functional, generalized free-weighting-matrix approach and Finsler’s lemma. Moreover, as a special case, an asymptotic stability criterion is obtained and used in a comparative study. As a result, the time-delay interval is much larger than some of the works published very recently, which is due to the augmented Lyapunov–Krasovskii functional construction. In addition, the effectiveness and practicability of the theoretical findings are validated with simulation examples. [ABSTRACT FROM AUTHOR]

The fundamental objective of this study is to focus on the control design for a class of Takagi–Sugeno fuzzy chaotic semi-Markov jump systems afflicted with multi-source disturbances. With an intention to portray more actual dynamical characteristics of the considered system, the actuator faults, partially unknown transition probabilities, randomly occurring uncertainties and gain fluctuations are considered. In particular, the multi-source disturbances are classified into matched and mismatched disturbances. Notably, the matched disturbances generated by systems whose dynamics are expressed in state-space form which are estimated with the construction of disturbance observers. Further, extended dissipative performance is intended to minimize the impact of mismatched disturbances. Specifically, a composite resilient reliable control scheme is put forward for synthesizing state feedback controller and output of the disturbance observers with the aim of rejecting and attenuating the aforementioned disturbances. On the strength of Lyapunov stability theory and linear matrix inequality concepts, a group of sufficient conditions is acquired to ensure that the assayed closed-loop systems and disturbance estimation error systems are stochastically stable. After that, the explicit forms of the composite controller and disturbance observers that adhere to the developed stability conditions are precisely expressed. To this end, the developed theoretical results are then applied to a standard Chua's circuit model, which aids in validating its effectiveness and usability. [ABSTRACT FROM AUTHOR]

The robust stabilization problem for singular fractional order time delay T-S fuzzy systems with nonlinearities and unknown external disturbances is addressed in this paper. An equivalent-input-disturbance (EID) estimator is used to estimate the impact of external disturbances and nonlinearities on the system output. Based on this EID approach, a dynamic compensator is designed to solve the stabilization problem of the considered system. Moreover, by considering a relevant Lyapunov-Krasovskii functional candidate and by using Lyapunov technique, the stability conditions in terms of LMIs are acquired for the considered closed-loop system. At last, to validate the effectiveness of the proposed result, two numerical examples are provided. [ABSTRACT FROM AUTHOR]

This paper gives attention to the issues of output tracking and disturbance rejection performance for a class of fractional order Takagi–Sugeno fuzzy systems in the presence of time-varying delay and unknown external disturbances. More specifically, a new configuration of a fractional order modified repetitive controller that incorporates an improved equivalent-input-disturbance estimator and gain fluctuations in its design is proposed to perform disturbance rejection for the addressed system. By introducing a continuous frequency distributed equivalent model and using the Lyapunov–Krasovskii stability theory, a new set of sufficient conditions ensuring robust asymptotic stability of the resulting closed-loop system is obtained in the framework of linear matrix inequalities. Finally, a numerical example is presented to validate the developed theoretical results, where it is shown that the obtained conditions could force the considered system output to exactly track the given any kind of reference signal by compensating the unknown external disturbance. • An output tracking problem is considered for fractional order TS fuzzy systems. • Repetitive control is designed to enhance the robustness of the considered systems. • Designed EID based controller effectively estimate and attenuate the disturbances. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the reliable non-fragile H ∞ control design problem for a class of discrete-time interval-valued fuzzy systems with actuator faults. More precisely, the actuator fault model considered in the controller design consists of linear and nonlinear fault terms. The main focus of this paper is to design a non-fragile state feedback controller that is characterized by membership functions described by upper and lower membership functions and nonlinear weighting functions. It should be mentioned that the proposed interval-valued fuzzy system and the controller do not share same membership functions. A novel set of sufficient conditions is obtained by transforming the controller design problem into a multi-objective convex optimization problem based on the linear matrix inequality and the Lyapunov functional approaches, which ensures the robust asymptotic stability of the addressed system with a desired H ∞ performance index. Finally, two numerical examples, including an application-oriented model, mass-spring-damping system are presented to demonstrate the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

This study investigates the non-fragile sampled-data guaranteed cost control problem for a bio-economic singular Markovian jump system that is represented by the Takagi-Sugeno fuzzy model. The main intention of this study is to design a non-fragile sampled-data controller for the considered model to handle the issue of tax fluctuations by means of showing that the closed-loop system is regular, impulse free and stochastically finite-time bounded. Sampled-data controller is the one where the continuous system is controlled by the digital control algorithms. By introducing a proper Lyapunov-Krasovskii functional and using linear matrix inequality (LMI) approach, a new set of criteria is obtained in terms of LMIs for achieving the required result. More precisely, by solving LMIs, an upper bound for the cost function can be obtained. Finally, a simulation result is given to illustrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the β -dissipativity-based reliable non-fragile sampled-data control problem for a class of interval type-2 (IT2) fuzzy systems. In particular, it is allowed to have randomly occurring time-varying delays in the controller design, which are modeled by Bernoulli distributed white noise sequences. Precisely, the IT2 fuzzy model and the non-fragile sampled-data controller are formulated by considering the mismatched membership functions. By constructing an appropriate Lyapunov–Krasovskii functional, a set of delay-dependent conditions is derived to guarantee that the closed-loop IT2 fuzzy system is strictly < Q,S,R > - β -dissipative. Moreover, the gain matrices of feedback reliable non-fragile sampled-data controller are derived in terms of linear matrix inequalities (LMIs), which can be solved by using existing LMI solvers. Two numerical examples are eventually given to illustrate the applicability and effectiveness of the proposed controller design technique. Highlights • An interval type 2 fuzzy model is formulated with upper and lower membership functions such that it can capture the uncertainties subject to probabilistic delay, actuator faults and gain fluctuations in the control design. • A generalized actuator fault model containing both linear and nonlinear terms is implemented in the non-fragile sampled-data controller design and the proposed controller precisely deals with the gain fluctuations. • By constructing an appropriate Lyapunov–Krasovskii functional together with Wirtinger-based double integral inequality, a new set of sufficient criteria is developed for obtaining the required result. • The obtained results are verified through numerical examples, which reveal that the proposed method yields less conservative results and better performance for the considered interval type 2 fuzzy model. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust finite time extended passive reliable filtering for Takagi-Sugeno (T-S) fuzzy systems with randomly occurring uncertainties, missing measurements, and time-varying delays. Moreover, two stochastic variables satisfying the Bernoulli random distribution are introduced to characterize the phenomenon of the randomly occurring uncertainties and missing measurements. By skillfully choosing a proper Lyapunov-Krasovskii functional (LKF), a new set of sufficient conditions in terms of linear matrix inequalities (LMI) is derived to ensure that the filtering error system is robustly stochastically finite time bounded (SFTB) with a desired extended passive performance index. Based on the obtained sufficient conditions, an explicit expression for the desired filter can be computed. Finally, two numerical examples are provided to show the effectiveness of the proposed filter design technique. [ABSTRACT FROM AUTHOR]

This study proposes a finite-time anti-disturbance observer-based reliable (Q , S , R) − θ dissipative feedback control technique for a class of Takagi-Sugeno fuzzy switched systems in conjunction with time-varying state/input delays and multiple disturbances. In contrast to previous findings, the external disturbances in this study are considered to be multiple disturbances, which are classified into matched and mismatched disturbances since the underlying system can be affected by various forms of disturbances [21] , [25]. In order to deal with the matched disturbances that are brought about by exogenous systems, an anti-disturbance observer has been established. As well, (Q , S , R) − θ dissipative performance handles the mismatched part, which includes the concepts of H ∞ , passivity, mixed H ∞ and passivity performance in a unified structure. In addition, unlike previous works in which the failure of the actuator is assumed to be deterministic [37] , [38] , the failure probability of the actuator in this work is determined using a distinct random variable with a probabilistic distribution in the range of [ 0 , 1 ]. Furthermore, in accordance with parallel distributed compensation method and reliable control design with stochastic theory, the desired fuzzy-rule based control protocol is developed. Moreover, distinct from the asymptotic and exponential stability that are defined over an infinite interval of time [4] , [14] , the finite-time notion is considered in this work, where it prevents the states from exceeding a specific range within a fixed interval. A set of adequate requirements are derived utilising the Lyapunov stability theory and average dwell time technique to ensure the finite-time boundedness of the system under consideration. In the end, effectiveness of the theoretical findings is validated by means of simulation results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of finite-time passivity-based H ∞ resilient reliable state feedback sampled-data control for Takagi–Sugeno fuzzy systems with randomly occurring uncertainties and gain variations, where the randomly occurring characteristics are designed by stochastic variables satisfying the Bernoulli distribution. The main objective of this paper is to design a resilient reliable sampled-data controller such that the resulting closed-loop system is finite-time bounded and satisfies finite-time mixed H ∞ and passive performance index γ . Based on the constructed Lyapunov–Krasovskii functional and Wirtinger integral inequality, some delay-dependent sufficient conditions are derived for achieving the required result of the considered systems. Moreover the derived finite-time stability conditions are established in the form of linear matrix inequalities (LMIs) which can be solved by Matlab LMI toolbox. Finally two numerical examples are presented to demonstrate the applicability of the proposed control design technique. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of disturbance rejection for a class of interval type-2 (IT-2) fuzzy systems via equivalence-input-disturbance (EID)-based approach. The main objective of this work is to design a fuzzy state-feedback controller combined with a disturbance estimator such that the output of the fuzzy system perfectly tracks the given reference signal without steady-state error and produces an EID to eliminate the influence of the actual disturbances. By constructing a suitable Lyapunov function and using linear matrix inequality (LMI) technique, a new set of sufficient conditions is established in terms of linear matrix inequalities for the existence of fuzzy controller. Finally, a simple pendulum model is considered to illustrate the effectiveness and applicability of the proposed EID-based control design. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust stabilization for a class of discrete-time Takagi-Sugeno (TS) fuzzy systems via input random delays in control input. The main objective of this paper is to design a state feedback H∞ controller. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov-Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust H∞ controller. In particular, the effect of both variation range and distribution probability of the time delay is taken into account in the control input. The key feature of the proposed results in this paper is that the time‐varying delay in the control input not only dependent on the bound but also the distribution probability of the time delay. The obtained results are formulated in terms of LMIs which can be easily solved by using the standard optimization algorithms. Finally, a numerical example with simulation result is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time mixedH∞and passivity performance analysis and filter design for a class of uncertain nonlinear discrete-time Markovian jump systems (MJSs) described by Takagi–Sugeno fuzzy model with nonhomogeneous jump processes. In this paper, the proposed MJSs fuzzy model is formulated with norm-bounded parameter uncertainties and time-varying jump transition probability matrices. In particular, the time-varying transition probability matrices are expressed in respect of a polytope. By constructing a suitable Lyapunov functional, a new set of sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to ensure that the filtering error system is robustly stochastically finite-time bounded and a prescribed mixedH∞and passive performance index is achieved. Moreover, the robust mixedH∞and passivity filter design gain matrices can be computed from the obtained LMIs. Furthermore, the developed results unifyH∞and passive filtering problems in a single framework. Finally, two numerical examples including an application-oriented example are provided to demonstrate the effectiveness of the proposed filter design technique. [ABSTRACT FROM PUBLISHER]

This article studies the reliable robust stabilization problem for a class of uncertain Takagi–Sugeno (TS) fuzzy systems with time-varying delays. The delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form. By implementing a proper novel Lyapunov functional together with linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions is derived to guarantee the asymptotic stability of TS fuzzy system with a prescribed H ∞ performance index. Further, a reliable robust H ∞ control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain TS fuzzy system. Further, Schur complement and Jensen's integral inequality are used to simplify the derivation in the main results. The set of sufficient conditions is established using the relationship among the random time-varying delay and its lower and upper bounds, which can be easily solved by MATLAB LMI toolbox. Finally, an illustrative example based on the truck-trailer model is provided to show the effectiveness of the proposed new design technique. [ABSTRACT FROM AUTHOR]

In this paper, the robust reliable $$H_\infty $$ control problem has been investigated for a class of nonlinear discrete-time TS fuzzy systems with random delay. In particular, the proposed fuzzy system consists of local nonlinear models with set of fuzzy rules, but the conventional TS fuzzy systems has local linear models. Our attention is focused on the design of a feedback reliable nonlinear retarded control law to ensure the robust asymptotic stability for nonlinear discrete-time TS fuzzy system with admissible uncertainties as well as actuator failure cases and random delay. In particular, by using an input delay approach, the random delay with stochastic parameters in the system matrices is introduced in the system model. Based on the Lyapunov approach, firstly, a sufficient condition for asymptotic stability is proposed for TS fuzzy systems in the presence of actuator failures. Then, a robust reliable $$H_\infty $$ control is designed for the uncertain TS fuzzy system by solving a strict linear matrix inequalities using the available numerical software. Finally, a numerical example based on real-time ball and beam system is provided to validate the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of robust reliable H∞ control for a class of uncertain Talcagi-Sugeno (TS) fuzzy systems with actuator failures and time-varying delay. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance level. Based on the Lyapunov-Krasovskii functional (LKF) method together with linear matrix inequality (LMI) technique, a delay dependent sufficient condition is established in terms of LMls for the existence of robust reliable H∞ controller. When these LMIs are feasible, a robust reliable H∞ controller can he obtained. Finally, two numerical examples with simulation result are utilized to illustrate the applicability and effectiveness of our obtained result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic stability issue for a class of stochastic Takagi-Sugeno (TS) fuzzy systems with time-varying delays. Then, by utilizing a delay-fraction ing method, the stochastic analysis theory combined with the matrix inequality technique, a new set of sufficient condition in terms of linear matrix inequalities is pre-sented which ensures the asymptotic stability of the stochastic TS fuzzy systems with time-delays. The results obtained in this paper are delay-dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of passivity analysis issue for a class of fuzzy bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time varying delays. A set of sufficient conditions for the passiveness of the considered fuzzy BAM neural network model is derived in terms of linear matrix inequalities by using the delay fractioning technique together with the Lyapunov function approach. In addition, the uncertainties are inevitable in neural networks because of the existence of modeling errors and external disturbance. Further, this result is extended to study the robust passivity criteria for uncertain fuzzy BAM neural networks with time varying delays and uncertainties. These criteria are expressed in the form of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Two numerical examples are provided to demonstrate the effectiveness of the obtained results. [Copyright &y& Elsevier]

This study addresses the issue of robust H∞ control for a class of uncertain Takagi-Sugeno fuzzy systems with distributed time delay and non-linear perturbations. By employing a new Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) technique, a new set of delay-dependent conditions are derived to achieve the robust stabilisation of uncertain fuzzy systems for a prescribed disturbance attenuation level γ > 0. The state feedback H∞ control law can be obtained by solving the corresponding LMIs. Further, some numerical examples are provided to demonstrate the effectiveness of the obtained results. The results reveal that the proposed theory significantly improve the allowable upper bounds of the delays over some existing results. [ABSTRACT FROM AUTHOR]

Abstract: This Letter addresses the stability analysis problem for a class of uncertain discrete-time stochastic fuzzy neural networks (DSFNNs) with time-varying delays. By constructing a new Lyapunov–Krasovskii functional combined with the free weighting matrix technique, a new set of delay-dependent sufficient conditions for the robust exponential stability of the considered DSFNNs is established in terms of Linear Matrix Inequalities (LMIs). Finally, numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained theory. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of passivity analysis for a class of Cohen–Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen–Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result. [Copyright &y& Elsevier]

This paper proposes an integrated robust stabilization and anti-disturbance control scheme for nonlinear systems using a polynomial fuzzy model approach. To estimate unknown disturbances, an equivalent-input-disturbance (EID) estimator is employed. The proposed approach incorporates a novel fuzzy model assisted by EID estimator into the sum-of-squares-based approach, utilizing a polynomial fuzzy model-based observer to estimate the disturbance effect. A suitable fuzzy rule-based control law is developed by utilizing the parallel distributed compensation approach and the output of the EID estimator. To ensure stability, fuzzy membership functions are converted into sum-of-square polynomials using a polynomial curve fitting approach, allowing their exact shape information to be used in the stability condition. The addressed system is transformed into an augmented system by incorporating the system, observer, and filter states, simplifying the analysis. Gain matrices for the controller and observer are obtained using Lyapunov stability theory and sum-of-squares methods to confirm asymptotic stabilization of the fuzzy system. Two numerical examples are presented to demonstrate the effectiveness of the proposed control design method. [ABSTRACT FROM AUTHOR]

This paper focuses on the robust H ∞ fault-tolerant control issue for a family of polynomial fuzzy systems subject to actuator faults and external disturbances. Especially, asynchronous fuzzy membership function technique is considered to minimize the expenses of controller implementation. To derive the robust stability conditions, actuator fault factors are taken into the account in the closed-loop system formulation. Moreover, to utilize the exact shape information of fuzzy membership functions in the stability criterion, they are approximated as sum-of-square polynomials with the aid of polynomial curve fitting method. In addition, to reduce the conservatism, a generalized polynomial Lyapunov function is considered. However, there are some non-convex terms in the stability conditions due to the construction of the generalized Lyapunov function that consists of all state-dependent polynomial matrix. Thus, some existing convex methods for general polynomial fuzzy systems are rendered inapplicable. To deal with this issue, the actual non-convex stability conditions converts into a convex optimization problem by introducing some additional convex constraints. Moreover, the membership-function-dependent robust stability conditions of the closed-loop system are provided as sum-of-square convex polynomial constraints. Lastly, the usefulness and superiority of the designed controller are illustrated by the simulation examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of fault-tolerant control for discrete-time interval type-2 (IT2) fuzzy time delay system with actuator faults under imperfect premise matching. The time-varying delay and actuator fault are first taken into account for the IT2 fuzzy discrete-time systems. The novel IT2 state-feedback controller and the IT2 fuzzy model share different lower and upper membership functions. The fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system under the actuator failures. Furthermore, the standard IT2 state-feedback controller is designed such that the closed-loop system is asymptotically stable and has an H ∞ performance. The obtained conditions of the fault-tolerant controller and the standard IT2 controller can be expressed by the convex optimization problems. A numerical example is presented to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

• The estimator of the addressed system is designed by introducing new membership functions and then by using the same premises of the observer, the fuzzy controller is designed. To be precise, sampling-based event-triggered scheme is taken into the account in the controller design to save the communication resources and avoid the existence of Zeno behaviour. • Furthermore, to compensate the impact of unknown disturbance, the equivalent-input-disturbance estimator-block is included as an internal loop of closed-loop system. To derive the stability conditions, a novel type of sampling-dependent piece-wise Lyapunov-Krasovskii functional is constructed. The problem of robust stabilization of interval type-2 fuzzy systems are studied by using equivalent-input-disturbance estimator-based event-triggered fuzzy control scheme. The estimator of the addressed system is designed by introducing new membership functions and then by using the same premises of the observer, the fuzzy controller is designed. To be precise, sampling-based event-triggered scheme is taken into the account in the controller design to save the communication resources and avoid the existence of Zeno behaviour. Furthermore, to compensate the impact of unknown disturbance, the equivalent-input-disturbance estimator-block is included as an internal loop of closed-loop system. To derive the stability conditions, a novel type of sampling-dependent piece-wise Lyapunov-Krasovskii functional is constructed. Then, by introducing slack matrices, the fuzzy membership function dependent stability criteria are derived. The event-triggered weighting matrix and the gains of controller and observer can be obtained by obtaining the solutions of the developed stability criteria. At last, numerical simulations are given to reflect the effectiveness and applicability of the developed theoretical results. [ABSTRACT FROM AUTHOR]