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The issues of input-output finite-time stability and stabilization of Takagi-Sugeno fuzzy systems with time-varying state delay and exogenous input signal are studied in this work. 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.

In this work, the problem of fault and state estimation is studied for Takagi-Sugeno fuzzy systems with time-varying delay and external disturbance over a finite horizon. A fuzzy rule-based fault estimator with two tuning parameters, including the current system output information, is designed. Based on which, the Luenberger state observer is then considered to estimate the immeasurable states of the system addressed. The aim of taking into account the tuning parameters in the estimator design is to improve the accuracy of the fault estimation. More precisely, by defining error variables in accordance with actual and estimated system states and faults, an augmented system is formulated to achieve the desired results. By using the existing stability theory and integral inequality, a delay-dependent criterion for ensuring that the states of the augmented system are bounded over a finite horizon is derived. Subsequently, conditions for determining the observer gain matrices are presented. Two simulation examples, including an application example of the truck-trailer model, are provided to demonstrate the advantages of the theoretical results that have been established. In particular, the importance of the use of tuning parameters is discussed.

This article intends to provide an integrated robust synchronization and anti-disturbance control design for a nonlinear multiweighted complex network with the use of fuzzy modeling approach. The network takes the effect of both matched and mismatched disturbances into account, wherein the matched one is unknown and caused by some exogenous systems. In order to estimate the unknown disturbance, a disturbance observer is precisely considered. By exploiting the parallel distributed compensation strategy and the output of disturbance observer, the desired fuzzy rule-based control law is formulated. Based on these settings, the required control gain matrices that affirm asymptotic synchronization of the addressed network are determined with the support of the Lyapunov functional method and extended Wirtinger’s integral inequality. The method of this article can render better system performance than the existing $H_{\infty }$ control method, which is demonstrated via simulations. In addition, a three-dimensional Lorenz chaotic model is employed to certify the applicability of the theoretical findings.

The aim of this article is to analyze the problem of fault estimation for mode-dependent interval type-2 fuzzy systems with quantized output measurements. Different from the existing fault estimation methods requiring the observer matching condition, a new fault estimation technique is proposed, wherein a stochastically intermediate variable subject to the information on operating modes is considered, under which a robust observer is constructed to simultaneously estimate the state and faults. Based on the strategy of linear matrix inequality, sufficient conditions are established to ensure that the states of resulting systems are bounded in probability sense. By offering three illustrative examples, in which two of them are practical models, namely, tunnel diode circuit system and Rossler system, the availability and feasibility of the proposed design method are explained.

This study focuses on the memory state feedback control problem for a family of time delayed interval type-2 Takagi-Sugeno fuzzy systems with external disturbance and actuator faulty input. Notably...

This study considers the uncertainty and disturbance estimator-based control problem for interval type-2 fuzzy stochastic systems with disturbances. The proposed control approach accurately estimates system unknown delays, uncertainties, non-linearities and external disturbances by introducing an appropriate filter. Precisely, the filter's bandwidth is one of the most important parameters in designing and tuning the controller to deal with unknown delays, uncertainties, non-linearities and disturbances. By using the Lyapunov–Krasovskii stability theorem and the linear matrix inequality approach, the required stability conditions and the control gain matrices for the system under consideration are obtained. Further, the effectiveness of the proposed control law is verified using two numerical examples.

This paper is concerned with the issue of finite-time boundedness of discrete-time uncertain interval type-2 fuzzy systems with time-varying delay and external disturbances via an observer-based reliable control strategy. According to the system output variable, a full-state observer that shares the same membership functions of the plant is constructed to estimate the unknown system states. In addition, a reliable controller subject to observer states and actuator faults is designed to formulate the closed-loop feedback control system, which does not share the same membership functions of the plant. Then, by constructing an appropriate Lyapunov–Krasovskii functional and using the finite-time stability theory, a new set of delay-dependent sufficient conditions guaranteeing the finite-time boundedness of the addressed system is established in the framework of linear matrix inequalities. Furthermore, the explicit expressions of gain matrices of the state observer and the reliable controller are given in terms of the established sufficient conditions. Finally, simulation results are presented to demonstrate the effectiveness of the obtained theoretical results.

This paper discusses the problem of stabilization of interval type-2 fuzzy systems with uncertainties, time delay and external disturbance using a dynamic sliding mode controller. The sliding surface function, which is based on both the system's state and control input vectors, is used during the control design process. The sliding mode dynamics are presented by defining a new vector that augments the system state and control vectors. First, the reachability of the addressed sliding mode surface is demonstrated. Second, the required sufficient conditions for the system's stability and the proposed control design are derived by using extended dissipative theory and an asymmetric Lyapunov-Krasovskii functional approach. Unlike some existing sliding mode control designs, the one proposed in this paper does not require the control coefficient matrices of all linear subsystems to be the same, reducing the method's conservatism. Finally, numerical examples are provided to demonstrate the viability and superiority of the proposed design method.

A robust tracking control design problem for a class of linear multi-agent systems with fault signals is addressed in this study, where it is assumed that input signal of the leader is non-zero and unknown to the follower agents. An intermediate estimator, which bears stochastic failures, is designed to achieve the desired tracking performance and to estimate the combined unknown input signal of the leader input and the fault terms simultaneously. Assisted by the estimated terms, a robust non-fragile tracking control protocol that takes into account communication delays is proposed to eliminate the influence of the combined input signal. With the help of the Lyapunov-Krasovskii functional approach, a delay-dependent sufficient criterion is established to ensure that the resulting tracking error system states are uniformly bounded. On the basis of this criterion, the design procedure of the considered non-fragile control gain and the intermediate estimator gain matrices are presented. Two numerical examples, including a practical example, are used to reflect the validity and usefulness of the designed tracking control protocol.

This paper concentrates on solving the finite-time bounded control problem for a family of discrete-time Takagi–Sugeno fuzzy Markov jump systems with a memory state feedback controller. In the proposed controller design, the non-fragile control protocol is considered to overcome the effect of gain perturbations and a more practical actuator fault model is employed to tolerate the time-varying faults. With the aid of a mode-dependent Lyapunov–Krasovskii functional and the Abel lemma-based finite sum inequality, sufficient conditions ensuring the stochastic finite-time boundedness for the closed-loop system are derived in the framework of matrix inequalities. Under which, a desired extended passivity performance index is guaranteed for the system under consideration. The proposed memory state feedback controller gains are computed by solving the derived matrix inequalities. Further, the feasibility and virtue of obtained theoretical findings are illustrated through two practical models, namely, single link robot arm system and Henon system.