Fuzzy Time-delay Systems Research Articles

Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems

In this paper, the problem of reliable filter design with strict dissipativity has been investigated for a class of discrete-time T-S fuzzy time-delay systems. Our attention is focused on the design of a reliable filter to ensure a strictly dissipative performance for the filtering error system. Based on the reciprocally convex approach, firstly, a sufficient condition of reliable dissipativity analysis is proposed for T-S fuzzy systems with time-varying delays and sensor failures. Then, a reliable filter with strict dissipativity is designed by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, numerical examples are provided to illustrate the effectiveness of the developed techniques.

Stability analysis and decentralized H∞ control for time-delay fuzzy interconnected systems via fuzzy Lyapunov-Krasovskii functional

This paper is concerned with the stability analysis and H∞ fuzzy controller design of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists of N interconnected time-delay Takagi-SugenoT-S fuzzy subsystems and the delay-dependent stability analysis is based on the fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is shown that the delay-dependent stability of the time-delay fuzzy interconnected systems can be established if a fuzzy weighting-dependent Lyapunov-Krasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities LMIs that are numerically feasible. The decentralized H∞ controllers are also designed by solving a set of LMIs based on these fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is demonstrated via numerical examples that the stability and controller synthesis results based on fuzzy weighting-dependent Lyapunov-Krasovskii functionals are less conservative than those based on the common quadratic Lyapunov-Krasovskii functionals.

Delay-dependent robust H ∞ filter for T-S fuzzy time-delay systems with exponential stability

This paper deals with the problem of delay-dependent robust filter for T-S fuzzy time-delay systems with exponential stability. The purpose is to design filter parameters such that the filtering error system is exponentially stable and satisfies a prescribed performance. In terms of linear matrix inequalities (LMIS), some sufficient conditions for the solvability of this problem are presented. Thanks to the new filter, the obtained stability criterion is less conservative than the existing ones. Finally, three examples are provided to demonstrate the effectiveness and the superiority of the proposed design methods.

New delay dependent robust stability criteria for T-S fuzzy systems with constant delay

This paper deals with the problem of delay dependent robust stability for T-S fuzzy time delay systems. The approach based on constructing a new Lyapunov-Krasovskii functional by dividing uniformly the delay interval into N segment with N is positive integer, and using Finsler’s lemma. This new Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments. The perturbations considered are norm bounded, and the results are expressed in terms of linear matrix inequality (LMIs). Numerical examples are provided to show the effectiveness of the present method, compared with some recent previous ones.

New delay-dependent stability analysis for fuzzy time-delay interconnected systems

This paper investigates the delay-dependent stability of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists of interconnected continuous-time Takagi–Sugeno fuzzy subsystems. A stability criterion based on fuzzy Lyapunov–Krasovskii functional is proposed to guarantee the asymptotic stability of fuzzy time-delay interconnected systems. In the derivation process, some free fuzzy weighting matrices are introduced among the terms of the system equation to yield less conservative results. The proposed stability criterion can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Finally, two numerical examples are provided to demonstrate the effectiveness of the present method.

Fuzzy-PID Control and its Stability Analysis of Large Time-Delay Nonlinear Systems

Aiming at a kind of state unpredictability of the fuzzy input large time-delay systems, the author designs a fuzzy observer with the application of Parallel Distributed Compensation (PDC), puts forward the PID control method based on the fuzzy observer, and provides a new sufficient condition which guarantees the asymptotic stability of fuzzy large time-delay system. With the employment of generalized Lyapunov function and linear matrix inequality, this paper proves the asymptotic stability of fuzzy input large time-delay systems and offers the separation design algorithm to control and observe gain matrix. The simulation results of the experiment further verify the effectiveness of the methods and conditions raised in this paper.

Robust sliding control for mismatched uncertain fuzzy time-delay systems using linear matrix inequality approach

In this article, we propose a robust sliding control design method for uncertain time-delay systems that can be represented by Takagi–Sugeno fuzzy models. The uncertain fuzzy time-delay systems under consideration have mismatched parameter uncertainties in the state matrix and external disturbances. We derive existence conditions of linear sliding surfaces guaranteeing the asymptotic stability in terms of constrained linear matrix inequalities (LMIs). We present an LMI characterization of such sliding surfaces. Also, an LMI-based algorithm is given to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give two numerical design examples to show the effectiveness of the proposed method.

Hankel norm model approximation of Takagi–Sugeno fuzzy time-delay systems

This paper is concerned with the Hankel norm model approximation for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time delay. 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 with a Hankel norm performance but is also translated into a lower-dimensional system. By employing the modified delay partitioning method, a delay-dependent sufficient condition is developed for the asymptotic stability with a Hankel norm error performance for the error system. Then, the Hankel norm approximation problem is solved by employing the convex linearization approach, which casts the reduced-order model construction into a convex optimization problem subject to linear matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the proposed methods.

Takagi-Sugeno Bilinear Based Model Non-fragile Guaranteed Cost Fuzzy Controller Design

In this paper, non-fragile characteristics existingin control systems are studied, and the existing sufficientcondition for the non-fragile guaranteed cost control ratebased on Lyapunov stable theory are derived, which canensure the close-loop system asymptotically stability for anyallowed uncertainties, and that performance index of theclose-loop system doesn’t exceed some upper bound for agiven performance function with quadratic form. And wealso proposed the designing method for a novel non-fragileguaranteed cost fuzzy controller design for continuous timedelayfuzzy system based on Takagi-Sugeno bilinear model.In the last part, two simulation examples proved theeffectiveness of this novel proposed method

Robust observer-based H control for nonlinear T-S fuzzy time-delay systems

This paper considers the design problem of observer-based H output feedback control over the nonlinear Takagi-Sugeno (T-S) fuzzy systems with distributed delays．Firstly, delay-dependent sufficient conditions satisfy the H performance, are given for the stability analysis in terms of non-strict linear matrix inequality; then, the equivalent linear matrix inequality stability conditions can be obtained. Based on this, the solvable of the observer-based H output feedback control problem is proposed. Finally, a numerical example is given to illustrate the effectiveness of the design approach here.

Observer-Based Robust Control of Uncertain Switched Fuzzy Systems with Combined Switching Controller

The observer-based robust control for a class of switched fuzzy (SF) time-delay systems involving uncertainties and external disturbances is investigated in this paper. A switched fuzzy system, which differs from existing ones, is firstly employed to describe a nonlinear system. Next, a combined switching controller is proposed. The designed controller based on the observer instead of the state information integrates the advantages of both the switching controllers and the supplementary controllers but eliminates their disadvantages. The proposed controller provides good performance during the transient period, and the chattering effect is removed when the system state approaches the origin. Sufficient condition for the solvability of the robust control problem is given for the case that the state of system is not available. Since convex combination techniques are used to derive the delay-independent criteria, some subsystems are allowed to be unstable. Finally, various comparisons of the elaborated examples are conducted to demonstrate the effectiveness of the proposed control design approach.

RobustH∞Control of Uncertain T-S Fuzzy Time-Delay System: A Delay Decomposition Approach

This paper is concerned with the problem of robustH∞control for a class of uncertain time-delay fuzzy systems with norm-bounded parameter uncertainties. By utilizing the instrumental idea of delay decomposition, the decomposed Lyapunov-Krasovskii functional is introduced to uncertain T-S fuzzy system, and some delay-dependent conditions for the existence of robust controller are formulated in the form of linear matrix inequalities (LMIs). When these LMIs are feasible, a controller is presented. A numerical example is given to demonstrate the effectiveness of the proposed method.

RobustH∞Control for a Class of Uncertain Switched Fuzzy Time-Delay Systems Based on T-S Models

The problem of robustH∞control for a class of uncertain switched fuzzy time-delay systems is discussed for system described by T-S fuzzy model with Lyapunov stable theory and linear matrix inequality approach. A sufficient condition in terms of the LMI is derived such that the stability of the closed-loop systems is guaranteed. The continuous state feedback controller is built to ensure the asymptotically stable closed-loop system for all allowable uncertainties, with the switching law designed to implement the global asymptotic stability of uncertain switched fuzzy time-delay systems. In this model, each and every subsystem of the switched systems is an uncertain fuzzy one to which the parallel distributed compensation (PDC) controller of each sub fuzzy system system is proposed with its main condition given in a more solvable form of convex combinations. Such a switched control system is highly robust to varying parameters. A simulation shows the feasibility and effectiveness of the design method.

New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching

To alleviate the conservativeness of the stability criterion for Takagi-Sugeno (T-S) fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from (34.299 2, 38.560 3) to (10.073 3, 11.349 0), respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x(0)=[3 −1]

Switching Control for a Class of Switched Fuzzy Time-delay Systems

Switching Control for a Class of Switched Fuzzy Time-delay Systems

Robust Reliable Control for a Class of Uncertain Time-Delay Switched Fuzzy Systems Based on Observers Switching

It is presented a model of uncertain time-delay switched fuzzy systems, which each subsystem of switched system is an uncertain time-delay fuzzy system. The robust reliable control problem is studied by multi-Lyapunov functions. When the actuators are serious failure – the residual part of actuators can not make original system stability, using switching technique depend on the states of observers, robust fuzzy reliable controller is built to ensure the relevant closed-loop system is asymptotic stability. The results for example are used to illustrate the feasibility and the effectiveness of the method.

Adaptive fuzzy H ∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems

In this paper, a fuzzy logic controller equipped with training algorithms is developed such that the H∞ tracking performance should be satisfied for a model-free nonlinear fractional order time delay system which is infinite dimensional in nature and time delay is a source of instability. In order to deal with the linguistic uncertainties caused from delay terms, the adaptive time delay fuzzy logic system is constructed to approximate the unknown time delay system functions. By incorporating Lyapunov stability criterion with H∞ tracking design technique, the free parameters of the adaptive fuzzy controller can be tuned on line by output feedback control law and adaptive law. Moreover, the tracking error and external disturbance can be attenuated to arbitrary desired level. The numerical results show the effectiveness of the proposed adaptive H∞ tracking scheme.

Novel stability and stabilization criteria for Takagi—Sugeno fuzzy time-delay systems

We study the problems of stability and stabilization for Takagi—Sugeno (T—S) fuzzy time-delay systems. First, by constructing a less-redundant Lyapunov—Krasovskii function and introducing a useful inequality, an innovative stability criterion is obtained, which gives a significant improvement on the performance. Compared with the exiting references, our result can use fewer unknown variables and get better results. Furthermore, based on the derived stability criteria, a new stabilization condition is developed, in which the controller gain and the maximum allowable delay bound can be obtained simultaneously. The conditions are all derived in the form of linear matrix inequality, which are easy to verify. Finally, numerical examples are given to show the effectiveness of the proposed methods.

Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach

This paper is concerned with robust sampled-data stabilization for uncertain fuzzy systems. The system is modeled as a continuous-time fuzzy system, while the control input is a zero-order sampled-data signal. When a zero-order control input is considered, the closed-loop system can be seen as an input delay system. Hence, an input delay system approach is introduced for sampled-data control design. Sufficient stability conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Under the assumption that sampling interval is not greater than some prescribed number, stability conditions for fuzzy time-delay systems are given by using Jensen’s Inequality, which simplifies conditions with less matrix variables. A design method of robust sampled-data state feedback controller for uncertain fuzzy systems is then proposed. Numerical examples are given to illustrate our robust sampled-data state feedback control design and to show the effectiveness over other existing results.

New Approach to Delay-Dependent Control for Fuzzy Time-Delay Systems

A new control method is proposed for stability analysis and stabilization problems for T-S fuzzy systems with time-delay. A new fuzzy Lyapunov-Krasovskii functional is introduced to establish some delay-dependent stability criteria. Based on parallel distributed compensation (PDC) scheme, a delay-dependent stabilization condition is derived and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples show that the effectiveness and benefits of the proposed method.