Uncertain Takagi-Sugeno Fuzzy Systems Research Articles

Robust Stabilization for Discrete Uncertain Takagi–Sugeno Fuzzy Systems Based on a Piecewise Lyapunov Function

This article investigates the robust H∞ fuzzy output-feedback control problem for a discrete Takagi–Sugeno (T–S) fuzzy system with uncertainties. By constructing a discrete piecewise Lyapunov function in each maximal overlapped-rule group, the systematic design of the fuzzy robust H∞ controller is studied through the parallel distributed compensation control scheme, and a new sufficient condition to check the robust asymptotic stabilization of the closed-loop discrete uncertain T–S fuzzy system is proposed and confirmed. This sufficient condition requires only finding common matrices in each maximal overlapped-rule group. Compared with the common Lyapunov function approach and the fuzzy Lyapunov function approach, the proposed sufficient condition can not only overcome the defect of finding common matrices in the whole feasible region but also significantly reduce the number of linear matrix inequalities to be solved. Therefore, the proposed condition is less conservative and difficult than the other two approaches. Finally, the simulation results for a class of two-echelon uncertain nonlinear supply chain systems show the effectiveness of the proposed approach.

A robust H∞-tracking design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using descriptor redundancy approach

This paper addresses a robust H∞ fuzzy observer-based tracking design problem for uncertain Takagi–Sugeno fuzzy systems with external disturbances. To have a practical observer-based controller, the premise variables of the system are assumed to be not measurable in general, which leads to a more complex design process. The tracker is synthesised based on a fuzzy Lyapunov function approach and non-parallel distributed compensation (non-PDC) scheme. Using the descriptor redundancy approach, the robust stability conditions are derived in the form of strict linear matrix inequalities (LMIs) even in the presence of uncertainties in the system, input, and output matrices simultaneously. Numerical simulations are provided to show the effectiveness of the proposed method.

Fault-Distribution Dependent Reliable H∞ Control for Takagi-Sugeno Fuzzy Systems

This paper is concerned with the problem of robust reliable H∞ control for a class of uncertain Takagi-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 LMIs for the existence of robust reliable H∞ controller. When these LMIs are feasible, a robust reliable H∞ controller can be obtained. Finally, two numerical examples with simulation result are utilized to illustrate the applicability and effectiveness of our obtained result.

Robust NonfragileH∞Filtering for Uncertain T-S Fuzzy Systems with Interval Delay: A New Delay Partitioning Approach

This paper investigates the problem of robust nonfragile fuzzyH∞filtering for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Attention is focused on the design of a filter such that the filtering error system preserves a prescribedH∞performance, where the filter to be designed is assumed to have gain perturbations. By developing a delay decomposition approach, both lower and upper bound information of the delayed plant states can be taken into full consideration; the proposed delay-fractional-dependent stability condition for the filter error systems is obtained based on the direct Lyapunov method allied with an appropriate and variable Lyapunov-Krasovskii functional choice and with tighter upper bound of some integral terms in the derivation process. Then, a new robust nonfragile fuzzyH∞filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are utilized to demonstrate the effectiveness and reduced conservatism of the proposed approach.

Robust Stability and Stabilization of Uncertain T–S Fuzzy Systems With Time-Varying Delay: An Input–Output Approach

An input-output approach to the stability and stabilization of uncertain Takagi-Sugeno (T-S) fuzzy systems with time-varying delay is proposed in this paper. The time-varying parameter uncertainties are assumed to be norm-bounded, and the delay is intervally time varying. A novel method is employed to approximate the time-varying delay, based on which the considered system is transformed into a feedback interconnection form. The new formulation of the system is comprised of a forward subsystem with constant time delay and a feedback subsystem embedding the uncertainties. By applying the scaled small-gain theorem to the converted system, less conservative stability and stabilization criteria are obtained. Moreover, the applicability of the proposed approach to the robust case is simpler since both delay and parameter uncertainties are processed in a unified framework. Numerical experiments are performed to illustrate the advantage of the proposed techniques.

Robust stabilisation of non-linear uncertain Takagi–Sugeno fuzzy systems by H∞ control

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.

Observer-based H∞ control for Takagi–Sugeno fuzzy systems with uncertainty and disturbance

This article is devoted to the design of a fuzzy-observer-based H∞ control for an uncertain Takagi–Sugeno fuzzy system with the existence of external disturbance and unavailable state variables. First, an augmented fuzzy model is built by integrating the system state with the output disturbance to create a new variable. Based on Lyapunov theory and linear matrix inequality tools, we derive sufficient conditions for the existence of the fuzzy-observer-based fuzzy controller guaranteeing a generalized H∞ performance level. A decoupled method is proposed in this study to transform the nonlinear matrix inequality (nonlinear matrix inequality) conditions into some LMI forms. Finally, the procedure of the fuzzy-observer-based H∞ control design is summarized and the effectiveness is demonstrated with a practical example.

Adaptive observer design for the uncertain Takagi–Sugeno fuzzy system with output disturbance

The study proposes an adaptive fuzzy observer for the uncertain Takagi–Sugeno (T–S) fuzzy system with output disturbance. First, an augmented fuzzy model is built by integrating the system state and the output disturbance together as new variables. Then, the desired adaptive fuzzy observer is designed to estimate the unavailable system state and the unknown output disturbance simultaneously. Based on Lyapunov theory and linear matrix inequalities (LMIs) tools, two main conditions are derived under which the fuzzy observer is designed. Finally, the procedure of the observer design is summarised and the effectiveness of the designed observer is demonstrated with a numerical example.

H∞ robust fuzzy dynamic observer-based controller for uncertain Takagi–Sugeno fuzzy systems

This study considers the problem of robust controller design for uncertain Takagi–Sugeno (T–S) fuzzy systems with H∞ performance through fuzzy dynamic observer (FDO). Dynamic observer is an alternative structure for classical observer which can be regarded as a general form of a usual observer and has additional degrees of freedom in the observer structure. In this study first the idea of dynamic observer in linear systems is extended to T–S fuzzy systems and it is shown that FDO can be used effectively for tackling the drawbacks of the existing methods of classical observer-based robust controller design. Strict linear matrix inequality (LMI) conditions are presented for designing robust H∞ observer-based controller even in the presence of uncertainties in system matrix, input and output matrices simultaneously by employing FDO. Finally, efficiency of the proposed design method is shown in simulation results.

Augmented Lyapunov–Krasovskii functional approaches to robust stability criteria for uncertain Takagi–Sugeno fuzzy systems with time-varying delays

This paper considers the problem of robust stability analysis for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. By constructing an augmented Lyapunov–Krasovskii functional and utilizing Finsler's Lemma, a novel criterion for delay-dependent robust stability of T–S fuzzy model with time-varying delay is derived in terms of linear matrix inequalities (LMIs). Also, a further improved stability criterion is proposed by utilizing free weighting techniques. Finally, three numerical examples are included to show the superiority of the proposed criteria.

Observer-based exponential stabilization of Takagi–Sugeno fuzzy systems with state and input delays

This paper proposes an exponential stabilization control method for uncertain Takagi–Sugeno fuzzy systems with state and input delays via output feedback. First, a unified memoryless fuzzy observer-based control method is introduced for stabilizing continuous and discrete uncertain time-delay fuzzy systems. Then, the exponential stability conditions are derived and converted to solving linear matrix inequality (LMI) problems. Based on the developed novel LMI algorithms, the controller and observer gains are able to be separately designed even in the presence of modelling uncertainty, state delay, and input delay. In comparison with existing techniques the proposed technique produces controlled states and state estimation errors that are guaranteed to exponentially converge to zero via output feedback. This is a major breakthrough for the control of uncertain systems with both state and input unavailable time-varying delays. Finally, two studies are carried out on continuous and discrete time-delay systems. Numerical simulation and comparison results demonstrate the quality of the obtained performance.

Observer-Based Robust $H_{\infty }$ Reliable Control for Uncertain T–S Fuzzy Systems With State Time Delay

In this paper, a method of robust H∞ reliable control for uncertain Takagi-Sugeno (T-S) fuzzy systems with unavailable states and time-varying delay is developed. In terms of linear-matrix inequalities (LMIs), we derive sufficient conditions for the existence of the fuzzy observer and the reliable fuzzy controller. The single-step LMI conditions, depending on the size of the delay, are proposed for the observer-based H∞ reliable controller design. This overcomes the drawback of two-step LMI approach in literature. Moreover, the designed fuzzy controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation but in the presence of some actuator faults as well. The result is given without the assumption of the rate of change of time-delay function (i.e., |τ| <; 1), which makes it applicable to both slow and fast time-varying delayed systems. Without considering reliability, the proposed result is much less conservative than most of the existing results. Finally, several examples are given to show the effectiveness and advantages of our results.

Delay-dependent non-fragile H ∞ filtering for uncertain fuzzy systems based on switching fuzzy model and piecewise Lyapunov function

This paper is concerned with the non-fragile H∞ filter design problem for uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay. To begin with, the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Then, based on the piecewise Lyapunov function and matrix decoupling technique, a new delay-dependent non-fragile H∞ filtering method is proposed for the switching fuzzy system. The proposed condition is less conservative than the previous results. Since only a set of LMIs is involved, the filter parameters can be solved directly. Finally, a design example is provided to illustrate the validity of the proposed method.

네트워크 제어 시스템의 강인 퍼지 관측기 기반 출력궤환 제어기

This paper discusses a robust observer-based output-feedback stabilization of an uncertain Takagi-Sugeno (T-S) fuzzy system in a network. In the networked control system, the input delay occurs inevitably and it is expressed by the Markovian stochastic process. To design robust sampled-data observer-based output-feedback controller, we discretize the T-S fuzzy system and represent as a jump system. Stochastic robust stabilization condition is formulated in terms of linear matrix inequalities.

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Generalized H2 (GH2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.

Delay-dependent robust H∞ control of convex polyhedral uncertain fuzzy systems

The robust H ∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H ∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities (LMIs). For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H ∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.

Robust Stability of Uncertain Takagi-Sugeno Fuzzy Systems with Time-varying Input-delay

This paper aims to design a controller to robustly stabilize uncertain Takagi-Sugeno fuzzy systems with time-varying input delay. Based on Lyapunov-Krasovskii functional approach, the sufficient conditions for robust stabilization of such systems are given in the form of linear matrix inequalities. The controller design does not have to require that the time-derivative of time-varying input delay be smaller than one. A numeric example is given to show that the proposed results are effective and less conservative.

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

Robust Output Feedback Guaranteed Cost Control of Uncertain Fuzzy Systems with Immeasurable Premise Variables

This paper is concerned with robust output feedback stabilization with guaranteed cost of uncertain Takagi-Sugeno fuzzy systems with immeasurable premise variables. When we consider Takagi-Sugeno fuzzy systems, the selection of premise variables plays an important role. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. However, the state is not measurable in the output feedback control problem. In this case, a control design based on parallel distributed compensation is impossible because a controller depends on immeasurable premise variables. In this paper, we consider the robust output feedback stabilization problem with guaranteed cost where the premise variable is not measurable. We formulate this problem as a robust stabilization of uncertain linear systems. Numerical examples are given to illustrate our theory.

H∞ control for uncertain Takagi–Sugeno fuzzy systems with time-varying delays and nonlinear perturbations

This paper investigates the robust H ∞ control for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays and nonlinear perturbations. Delay-dependent criteria for uncertain fuzzy systems have been proposed. The LMI optimization approach is applied to solve the H ∞ control problem and find the minimization of H ∞ norm bound. Computer simulations show that significant improvement over the previous results can be obtained.