Fuzzy Time-delay Systems Research Articles

A critical review of nonlinear fuzzy multiple time-delay interconnected systems using the Lyapunov criterion

This paper reviews the development of fuzzy systems and the problem of time delay control in nonlinear systems. Based on this review, a fuzzy Lyapunov method defined in fuzzy blending quadratic Lyapunov functions is proposed from which to derive stability conditions. In the controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller (FLC) by blending all linear local state feedback controllers. Furthermore, the multiple time-delay interconnected systems are considered in the nonlinear fuzzy systems. Key words: Interconnected systems, fuzzy Lyapunov method, linear matrix inequality.

A critical review of parallel distributed computing and the Lyapunov criterion for multiple time-delay fuzzy systems

This work reviews some important Lyapunov criterion results based on which we address the stability problems of multiple time-delay Takagi-Sugeno (T-S) fuzzy systems. A delay-dependent stability criterion is derived using the fuzzy Lyapunov method that will ensure the asymptotic stability of the multiple time-delay T-S fuzzy systems. Furthermore, the parallel distributed compensation (PDC) scheme is used to achieve a controller design for fuzzy systems. Key words: Lyapunov, critical review, multiple time-delay system, PDC.

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.

Adaptive Fuzzy Tracking Control for MIMO Uncertain Nonlinear Time-delay Systems

Abstract This paper addresses the problem of adaptive fuzzy tracking control for MIMO uncertain nonlinear time-delay systems. The control scheme combines adaptive fuzzy control with  H control. Adaptive time-delay fuzzy logic systems are constructed and used to approximate the uncertain unknown timedelay functions. The  H compensator is designed to eliminate fuzzy approximation errors and external disturbances. The adaptive laws for parameters are given by the tracking error. The timedelay Lyapunov function is constructed, and then it is proved that the error closed loop system satisfies the anticipant  H tracking performance. Simulation results demonstrate that the control scheme is feasible.

Fault detection for a class of network-based nonlinear systems with communication constraints and random packet dropouts

This paper is dealt with the fault detection (FD) problem for a class of network-based nonlinear systems with communication constraints and random packet dropouts. The plant is described by a Takagi–Sugeno fuzzy time-delay model, it has multiple sensors and only one of them is actually communicated with the FD filter at each transmission instant, and the packet dropouts occur randomly. The goal is to design a FD filter such that, for all unknown inputs, control inputs, time delays and incomplete data conditions, the estimation error between the residual and ‘fault’ (or, more generally, the weighted fault) is minimized. By casting the addressed FD problem into an auxiliary H∞ filtering problem of a stochastic switched fuzzy time-delay system, a sufficient condition for the existence of the desired FD filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique. Copyright © 2011 John Wiley & Sons, Ltd.

Improved adaptive fuzzy control for MIMO nonlinear time-delay systems

This paper presents an improved observer-based indirect adaptive fuzzy control scheme for multiinput-multioutput (MIMO) nonlinear time-delay systems. The control scheme synthesizes adaptive fuzzy control with adaptive fuzzy identification. An observer is designed to observe the system state, and an identifier is developed to identify the unknown parts of the system. The update laws for parameters utilize two types of errors in the adaptive time-delay fuzzy logic systems, the observation error and the identification error. Performance analysis proves the superiority of the update laws in terms of faster and improved tracking and parameter convergence. Simulation results of two-link manipulator demonstrate the effectiveness of the improved control scheme.

Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework

This paper is concerned with the problem of H∞ model approximation for discrete-time Takagi-Sugeno (T-S) fuzzy time-delay systems. For a given stable T- S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an H∞ performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an H∞ error performance for the error system. Then, the H∞ model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, H∞ model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Robust anti-windup controller design of time-delay fuzzy systems with actuator saturations

This study presents a robust anti-windup fuzzy control approach for uncertain nonlinear time-delay systems with actuator saturations. The discussed system dynamics is presented by the Takagi–Sugeno (T–S) fuzzy model. To facilitate the design process, the nonlinearity of input saturation is characterized by a specific sector condition. Given a stabilizing dynamic output feedback fuzzy controller, an anti-windup control approach is then developed to maximize the size of estimate of the domain of attraction. Significantly, the convergence of all admissible initial states within this region could be ensured. Based on the Lyapunov–Krasovskii delay-independent and delay-dependent analyses, sufficient conditions for the robust stabilization are derived. These conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities, allowing the fuzzy controller to be synthesized more efficiently. Finally, numeric simulations are given to validate the proposed approach.

Fuzzy Time-delay Dynamical Systems

This paper investigates the first order linear fuzzy time-delay dynamical systems. We use a complex number representation of the \(\alpha\)-level sets of the fuzzy time-delay system, and obtain the solution by applying a Runge-Kutta method. Several examples are considered to show the convergence and accuracy of the proposed method. We finally present some conclusions and new directions for further research in this area.

New Approach of Stability for Time-Delay Takagi-Sugeno Fuzzy System Based on Fuzzy Weighting-Dependent Lyapunov Functionals

This paper deals with the stability of Takagi-Sugeno fuzzy models with time delay. Using fuzzy weighting- dependent Lyapunov-Krasovskii functionals, new sufficient stability criteria are established in terms of Linear Matrix Inequality; hence the stability bound of upper bound delay time can be easily estimated. Finally, numeric simulations are given to validate the developed approach.

Nonfragile control for a class of uncertain switching fuzzy time-delay systems

A sufficient condition for the existence of nonfragile state-feedback controllers and a switching law for a class of uncertain switching fuzzy time-delay systems are proposed based on the multiple Lyapunov functions technique, under the assumption that the controller gain to be designed has variations. The corresponding results are all formulated in terms of linear matrix inequalities (LMIs). Simulation results show the effectiveness of the design method.

Robust [formula omitted] control for uncertain T–S fuzzy time-delay systems with sampled-data input and nonlinear perturbations

The H ∞ control for Takagi–Sugeno (T–S) fuzzy time-delay systems with sampled-data input and nonlinear perturbations is considered in this paper. In order to treat the sampled-data input problem, the time-varying delay transformation technique is provided to find the upper bound of sampled time. LMI optimization approach is applied to solve the H ∞ control problem and find the minimization of disturbance attenuation.

Delay-Dependent Nonfragile Robust H ∞ Filtering of T–S Fuzzy Time-Delay Systems

The problem of nonfragile robust H∞ filtering for a class of Takagi–Sugeno fuzzy time-delay systems is investigated in the paper. We design a fuzzy filter which can tolerate some level of the filter gain variations while ensuring both the robust stability and a prescribed H∞ performance level of the filtering error system. Delay-dependent sufficient conditions for the existence of such filters are obtained in terms of linear matrix inequalities, and an explicit expression of a desired filter is given.

Robust passivity and passification of stochastic fuzzy time-delay systems

In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Stability and Stabilization of Delayed T--S Fuzzy Systems: A Delay Partitioning Approach

This paper proposes a new approach, namely, the delay partitioning approach, to solving the problems of stability analysis and stabilization for continuous time-delay Takagi-Sugeno fuzzy systems. Based on the idea of delay fractioning, a new method is proposed for the delay-dependent stability analysis of fuzzy time-delay systems. Due to the instrumental idea of delay partitioning, the proposed stability condition is much less conservative than most of the existing results. The conservatism reduction becomes more obvious with the partitioning getting thinner. Based on this, the problem of stabilization via the so-called parallel distributed compensation scheme is also solved. Both the stability and stabilization results are further extended to time-delay fuzzy systems with time-varying parameter uncertainties. All the results are formulated in the form of linear matrix inequalities (LMIs), which can be readily solved via standard numerical software. The advantage of the results proposed in this paper lies in their reduced conservatism, as shown via detailed illustrative examples. The idea of delay partitioning is well demonstrated to be efficient for conservatism reduction and could be extended to solving other problems related to fuzzy delay systems.

H ∞ control of non-linear dynamic systems: a new fuzzy delay partitioning approach

The problem of robust H infin control for Takagi-Sugeno (T-S) fuzzy systems with norm-bounded parameter uncertainties and a time delay in the state is investigated. Attention is focused on the design of robust H infin controllers via the parallel distributed compensation scheme such that the closed-loop fuzzy time-delay system is asymptotically stable and the H infin disturbance attenuation is below a prescribed level. By utilising the instrumental idea of delay partitioning, a new Lyapunov-Krasovskii functional is introduced, and some novel ideas for achieving delay dependence and basis dependence have been employed, which guarantee the obtained conditions to be much less conservative than most existing results in the literature. These conditions are formulated in the form of linear matrix inequalities (LMIs), based on which, the controller design is cast into a convex optimisation problem subject to LMI constraints. Finally, two examples are illustrated to show the feasibility and effectiveness of the obtained results.

Robust [formula omitted] control of uncertain fuzzy systems under time-varying sampling

Robust H ∞ sampled-data control for uncertain fuzzy systems is discussed. In many practical situations, a system is modeled as a continuous-time fuzzy system, while the control input is the zero-order hold, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the H ∞ sampled-data control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, H ∞ performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using the Leibniz–Newton formula and free-weighting matrix method for fuzzy time-delay systems under the assumption that sampling time is not greater than some prescribed number. Then, a design method for a robust H ∞ sampled-data state feedback controller for uncertain fuzzy systems is proposed. Numerical examples are given to illustrate our robust H ∞ sampled-data state feedback control design.

Robust Guaranteed Cost Control of Uncertain Fuzzy Systems Under Sampled-Data Inputs

A dynamical system is usually modeled as a continuous-time system, while the control input is applied at discrete instants. This is called a sampled-data control system. This paper is concerned with robust sampled-data control with guaranteed cost for uncertain fuzzy systems. The sampled-data control input is usually the zero-order hold and hence has a piecewise-continuous delay. Thus, an input delay system approach to robust sampled-data control is introduced. Sufficient robust guaranteed cost performance conditions for the closed-loop system with a sampled-data state feedback controller are given in terms of linear matrix inequalities(LMIs). Such robust conditions are derived via descriptor approach to fuzzy time-delay systems under the assumption that a sampling interval may vary but is not greater than some prescribed number. A design method of robust sampled-data guaranteed cost controller for uncertain fuzzy systems. Numerical examples are given to illustrate our sampled-data state feedback control.

Control of Fuzzy Switched Time-Delay Uncertain Systems: An Improved Robust Output Feedback Design

AbstractRobust output feedback control for a class of switched uncertain time-delay fuzzy systems via both methods with common Lyapunov and multiple Lyapunov functions is studied in this paper. Using Parallel Distributed Compensation, observer estimators and a switching law, the fuzzy output feedback controllers are designed such that the corresponding closed-loop system possesses robustness for all admissible uncertainties. The solution inequalities are expressed in LMI. An illustrative example along with the respective simulation results is given to demonstrate the effectiveness of the proposed design.

Robust stabilization of uncertain T–S fuzzy time-delay systems with exponential estimates

This paper deals with the problem of robust stabilization for uncertain Takagi–Sugeno (T–S) fuzzy systems with constant time delays. The purpose is to design a state-feedback fuzzy controller such that the closed-loop system is robustly exponentially stable with a prescribed decay rate. Sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). By using feasible solutions of these LMIs, desired fuzzy controllers are designed and their corresponding exponential estimates are given. In addition, the main results of this paper are explicitly dependent on the decay rate. This enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions. Two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods.