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The problem of input–output stability analysis and stabilisation of discrete Takagi–Sugeno (T–S) fuzzy systems with a time-varying delay via an input–output (I–O) approach is investigated in this paper. Using a three-term approximation-based model, a forward subsystem with three constant delays and a feedback subsystem are presented. Two separate input–output stability criteria have been formulated, using an input–output approach and a scaled small gain theorem: a criterion based on the lifting method, a non-quadratic Lyapunov function, and bounded real lemma, another criterion based on a non-quadratic Lyapunov–krasovskii functional approach. Using this result, the input–output stabilisation problem is resolved through the so-called parallel distributed compensation (PDC) scheme. The conditions obtained are presented in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the advantages and merit of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This article concerns the estimation and tracking control problems for Takagi–Sugeno systems with disturbances and norm bounded uncertainties in presence of sensor and actuator faults (SAF). First, we propose a robust fuzzy observer (RFO) design method to estimate both state and SAF for the considered class of the nonlinear systems. Then, this RFO‐based fault tolerant tracking control is developed not only to compensate the SAF effects but also to ensure the state convergence to desired trajectories in spite of their presence. To reduce the conservatism of design conditions, observer and controller gains are calculated in a single step by solving a set of linear matrix inequality constraints. H∞ criterion is used to attenuate disturbance effects and to reduce the tracking error. Finally, simulation results by considering two types of actuator fault and comparative study on a single link flexible joint manipulator are provided to underline the performances of the mentioned process. [ABSTRACT FROM AUTHOR]

Summary: This article addresses the issue of delay‐dependent H∞ filtering design for TakagiŮSugeno fuzzy time‐varying delay systems using the input–output approach. A three‐term approximation model has been used to transform the original system into two interconnected subsystems. Since the nonquadratic Lyapunov–Krasovskii functional requires to deal with the membership function's (MF) time derivative, upper‐bound inequalities have been added to the obtained conditions. Based on the scaled small gain theorem, nonquadratic Lyapunov–Krasovskii functional approach and considering the bounds of the MF time‐derivative, the H∞ full‐ and reduced‐order filters are designed and then formulated in terms of linear matrix inequalities. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

In this work, we investigate the problem of control for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models affected by both sensor and actuator faults subject to an unknown bounded disturbances (UBD). For this, we design an adaptive observer to estimate state, sensor and actuator fault vectors simultaneously despite the presence of external disturbances. Based on this observer, we develop a fault tolerant control (FTC) law not only to stabilize closed loop system, but also to compensate the fault effects. For the observer-based controller design, we propose less conservative conditions formulated in terms of linear matrix inequalities (LMIs). Moreover, both observer and controller gains are calculated via solving a set of LMIs only in single step. Finally, comparative results and an application to single-link flexible joint robot are afforded to prove the efficiency of the proposed design. [ABSTRACT FROM AUTHOR]

This study deals with (Q,S,R) ‐ γ ‐dissipative output feedback control design for a class of switched systems with time‐varying delay and unmeasurable states. The purpose is to design an observer‐based controller and a switching rule to ensure both exponential stability and strict dissipativity of the resulting closed‐loop switched systems. Using an augmented switched Lyapunov–Krasovskii functional with triple sum and the improved reciprocally convex combination approach, new sufficient conditions are developed in terms of linear matrix inequalities. Simulation examples are included to demonstrate the validity and effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of state/fault estimation and active fault-tolerant control (AFTC) design for time-delay descriptor fuzzy systems subject to external disturbances and actuator faults. Using Takagi-Sugeno fuzzy models, an adaptive fuzzy observer is proposed to achieve system state and actuator fault estimation simultaneously. According to Lyapunov functional method, design and analysis conditions of the resulting closed-loop delayed descriptor system are formulated in terms of linear matrices inequalities (LMIs). Observer and controller gains are computed by solving a set of LMIs in only one step and then used to both estimate the unmeasured states and actuator faults in AFTC context. Numerical examples are provided to show the merit and the conservativeness of the proposed approach in comparison with the existing methods by considering various types of actuator faults. [ABSTRACT FROM AUTHOR]

This study investigates the problem of delay‐dependent stability and stabilisation of uncertain delta operator systems with time‐varying delay. A new model transformation is proposed using a three‐term approximation, which has a smaller approximation error than the existing methods based on one or two terms. On the basis of scaled small gain theorem (scaled small gain) and an appropriate Lyapunov–Krasovskii functional, a new stability criterion is proposed in terms of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the problem of H ∞ filter analysis and design for discrete-time Takagi–Sugeno (T-S) fuzzy systems, in a finite frequency (FF) domain. Based on a fuzzy basis dependent Lyapunov function and time domain interpretations of Generalized Kalman Yakubovich Popov (GKYP) lemma, combined with generalised S-procedure, sufficient conditions are developed, guaranteeing that the filtering error system is stable and has a prescribed H ∞ attenuation level, over a specified FF domain of the external disturbances. Furthermore, several additional slack variables are introduced to the derived conditions by applying Finsler’s lemma twice, which leads to performance improvement and less conservatism in the solution. Thus, new filter design conditions are proposed in the formulation of Linear Matrix Inequality (LMI) terms in three different frequency ranges, (low, middle and high frequencies). A numerical example is given to demonstrate the feasibility, the effectiveness and the less conservatism of the proposed approach in comparison with another solution that appears in the literature. [ABSTRACT FROM AUTHOR]

In this study, the analysis and design problems of H∞ filtering for a class of discrete‐time‐varying delay systems are investigated. The authors' attention is focused on the filter design using scaled small gain (SSG) approach guaranteeing the robust asymptotic stability of the filtering error system with a prescribed H∞ performance. A novel transformation model of the filtering error system is obtained via three‐term approximation method and input–output approach based on SSG theorem. Then, the desired filter design is obtained through a convex optimisation problem resolution under a set of linear matrix inequality constraints. Finally, the use of many examples from the literature demonstrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The problem of sliding-mode control (SMC) with dissipativity for a class of time-delay Takagi-Sugeno fuzzy singular systems is investigated. The system is subject to uncertainties and input non-linearity. Based on an integral sliding surface, a delay-dependent criterion is developed in terms of linear matrix inequalities, which ensures the sliding mode dynamics to be robustly admissible and strictly (Q, S,R)-dissipative. Moreover, an SMC law is established such that the reachability of the specified sliding surface is guaranteed. Finally, the validity and applicability of the proposed approach are illuminated by two simulation examples. [ABSTRACT FROM AUTHOR]

SUMMARY This paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time-delay. First, on the basis of the Lyapunov functional method and by resorting to the delay-partition technique, improved delay-dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse-free, and stable). Second, with the help of the obtained admissibility criterion, an observer-based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an H ∞ robust static output fuzzy controller for dc–dc converters using Takagi–Sugeno fuzzy models. In the proposed approach, the controller is designed using the output voltage which is the measured signal. Therefore, the number of sensors does not increase in comparison with traditional approaches. In addition, the proposed controller is designed to not only ensure a good reference tracking with disturbance rejection, but also provide the robustness with respect to the input voltage and load variations. The asymptotic tracking of signal is guaranteed, in the Lyapunov sense, by satisfying some sufficient conditions given in Linear Matrix Inequality form. Numerical examples show the good steady-state and dynamic behaviors. [Copyright &y& Elsevier]