Discrete-time Fuzzy Research Articles

Fuzzy Dynamic Output Feedback Control for T-S Fuzzy Discrete-Time Systems With Multiple Time-Varying Delays and Unmatched Disturbances

This paper addressed the fuzzy dynamic output feedback control problem for a class of nonlinear discrete-time Takagi–Sugeno (T-S) fuzzy systems with multiple time-varying delays and unmatched disturbances. Based on the control input matrix and output matrix, the T-S fuzzy model is employed to approximate the nonlinear discrete-time system. Based on the stochastic system theory and the Bernoulli distribution, the fuzzy dynamic output feedback controller is constructed for the nonlinear discrete-time T-S fuzzy system with multiple time-varying delay and unmatched disturbance. The $H_{\infty } $ performance analysis is presented, and the cone complementarity linearization algorithm is employed for the stability analysis to deal with the non-convex problem caused by the basis-dependent linear matrix inequalities conditions. Compared with the previous works, the developed controller in this paper is smooth and only uses the system output. The control design conditions are relaxed because of the developed cone complementarity linearization algorithm. The results are further extended to the chemical process case and the mobile robot case. Finally, two simulation examples are performed to show the effectiveness of the proposed methods.

Interval Observer-Based Fault Isolation for Discrete-Time Fuzzy Interconnected Systems With Unknown Interconnections.

This paper is concerned with the fault isolation problem for discrete-time fuzzy interconnected systems with unknown interconnections. First, for each subsystem, a fault isolation interval observer is constructed by taking into account the bounds of the unknown interconnections and subsystem disturbances. Then, l1 and H∞ performances are introduced to improve the tightness of the residual intervals and the sensitivity to their own faults, respectively. Furthermore, the fault isolation decision is made by determining whether the zero value is excluded from each residual interval. By utilizing the piecewise Lyapunov functions and dilated linear matrix inequalities, the obtained observer design conditions are less conservative than the existing results with the common and diagonal Lyapunov functions. Finally, simulation results are presented for showing the effectiveness and superiority of the proposed method.

Fuzzy-model-based admissibility analysis and output feedback control for nonlinear discrete-time systems with time-varying delay

This paper is concerned with the admissibility analysis and stabilization problems for singular fuzzy discrete-time systems with time-varying delay. The novelty of this paper comes from the consideration of a new summation inequality which is less conservative than the usual Jensen inequality, the Abel-Lemma based inequality and the Seuret inequality. Based on the inequality, sufficient conditions are established to ensure the systems to be admissible. Moreover, the corresponding conditions for the existence of desired static output feedback controller gains are derived to guarantee that the closed-loop system is admissible. The conditions can be solved by a modified cone complementarity linearization (CCL) algorithm. Examples are given to show the effectiveness of the proposed method.

Adaptive Discrete-time Fuzzy Sliding Mode Control For a Class of Chaotic Systems

Adaptive Discrete-time Fuzzy Sliding Mode Control For a Class of Chaotic Systems

Stability and Stabilization of a Class of Discrete-Time Fuzzy Systems With Semi-Markov Stochastic Uncertainties

This paper addresses the problems of stability and stabilization for a class of discrete-time Takagi–Sugeno fuzzy systems with semi-Markov stochastic uncertainties. By means of the semi-Markov kernel, the probability density function of the sojourn time for different modes in describing the underlying semi-Markov stochastic uncertainties can be mode-dependent in contrast with the previous studies. Both the sojourn-time-independent and sojourn-time-dependent Lyapunov functions are proposed, by which the stability criteria are obtained in terms of a new $\boldsymbol {\sigma }$ -error mean square stability concept, and the latter is demonstrated to be less conservative and more practical than some existing results. Then, control synthesis problem is investigated and the sufficient conditions on the existence of admissible mode-dependent state-feedback stabilizing controller are developed. A numerical example and a cart-pendulum system are given to show the effectiveness and potential of the new design techniques.

Resilient H∞ sliding mode control for discrete-time descriptor fuzzy systems with multiple time delays

ABSTRACTThe resilient sliding mode control (SMC) problem for a class of discrete-time descriptor Takagi–Sugeno (T-S) fuzzy systems with multiple state delays is addressed. Attention is focused on the design of a discrete-time SMC such that the admissibility as well as the H∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delays and external disturbances. Based on a new sliding function, a delay-dependent sufficient condition is established to ensure the desired performance of the sliding mode dynamics on the specified sliding mode surface. Moreover, a resilient SMC law is established to satisfy the reaching condition. Finally, two examples are given to show the effectiveness and advantages of the proposed design SMC scheme.

Finite-Time $H_{\infty }$ Filtering for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay and Norm-Bounded Uncertainties

In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are proposed and the filter gain matrices can be obtained by calculating a set of linear matrix inequalities. A numerical example is used to illustrate the effectiveness of the proposed approaches.

Stabilization of Discrete-time Fuzzy Systems Via Delta Operators and its Application to Truck–Trailer Model

This paper addresses the problem of robust $$L_2{-}L_\infty $$L2-L? control in delta domain for a class of Takagi---Sugeno (TS) fuzzy systems with interval time-varying delays and disturbance input. In particular, the system under study involves state time delay, uncertainties and fast sampling period $$\mathcal {T}$$T. The main aim of this work was to design a $$L_2{-}L_\infty $$L2-L? controller such that the proposed TS fuzzy system is robustly asymptotically stable with a $$L_2{-}L_\infty $$L2-L? prescribed performance level $$\gamma >0$$?>0. Based on the proper Lyapunov---Krasovskii functional (LKF) involving lower and upper bound of time delay and free-weighting technique, a new set of delay-dependent sufficient conditions in terms of linear matrix inequalities (LMIs) are established for obtaining the required result. The result reveals that the asymptotic stability is achieved quickly when the sampling frequency is high. Finally, a numerical example based on the truck---trailer model is given to demonstrate the effectiveness and potential of the proposed design technique.

Switching Control Design for Switched Fuzzy Discrete-Time Systems

This paper investigates the problems of stability analysis and stabilization for a class of switched fuzzy discrete-time systems. Based on a common Lyapunov functional, a switching control method has been developed for the stability analysis of switched discrete-time fuzzy systems. A new stabilization approach based on a switching parallel distributed compensation scheme is given for the closed-loop switched fuzzy systems. Finally, the illustrative example is provided to demonstrate the effectiveness of the techniques proposed in this paper.

Nonfragile Guaranteed Cost Control of Discrete-Time Fuzzy Bilinear System With Time-Delay

This paper focuses on the problem of nonfragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems (DFBS) with time-delay in both states and inputs. Based on the parallel distributed compensation approach, the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations.

State Estimation for Discrete-Time Fuzzy Cellular Neural Networks with Mixed Time Delays

This paper is concerned with the exponential state estimation problem for a class of discrete-time fuzzy cellular neural networks with mixed time delays. The main purpose is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. By constructing a novel Lyapunov-Krasovskii functional which contains a triple summation term, some sufficient conditions are derived to guarantee the existence of the state estimator. The linear matrix inequality approach is employed for the first time to deal with the fuzzy cellular neural networks in the discrete-time case. Compared with the present conditions in the form ofM-matrix, the results obtained in this paper are less conservative and can be checked readily by the MATLAB toolbox. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed results.

H∞Enhanced Control Design of Discrete-Time Takagi-Sugeno State-Multiplicative Noisy Systems

Design conditions for existence of theH∞state feedback control for Takagi-Sugeno fuzzy discrete-time stochastic systems with state-multiplicative noise, stabilizing the closed-loop in such way that the quadratic performance in the mean is satisfied, are presented in the paper. Using newly introduced enhanced form of the bounded real lemma for such stochastic systems, the LMI-based procedure is provided for computation of gain matrices of the state control law, realized in the parallel distributed compensation structure. The approach is illustrated on an example, demonstrating the validity of the proposed method.

Discrete-Time Fuzzy Speed Regulator Design for PM Synchronous Motor

This paper proposes a discrete-time Takagi-Sugeno (T-S) fuzzy speed regulator system for a permanent-magnet synchronous motor (PMSM). An accurate approximate discrete-time T-S fuzzy model is first derived for a PMSM. By using the discrete-time T-S fuzzy model, a fuzzy acceleration observer as well as a fuzzy speed regulator is designed. In terms of linear matrix inequalities, sufficient conditions for the existence of the regulator and observer are derived. The exponential stability of the augmented control system is also shown. The proposed discrete-time T-S fuzzy speed regulator system is implemented by using a TMS320F28335 floating point DSP. Simulation and experimental results are given to verify that the proposed digital control method can be successfully used for a PMSM under model parameter and load torque variations.

Observer-based Control of Discrete-Time Fuzzy Positive Systems with Time Delays

Abstract This paper presents a stabilization approach for discrete-time nonlinear positive systems with delays via T-S fuzzy model which is developed for both state feedback and observer-based output feedback cases. The state feedback controller is designed based on trajectory approach. The observer-based controller design is obtained based on linear copositive Lyapunov functional and the trajectory approach. The proposed stabilization conditions are formulated in terms of linear programs(LPs), which can be solved efficiently by using existing optimization techniques.

Control Design for Discrete-Time Fuzzy Systems with Disturbance Inputs via Delta Operator Approach

This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a state-feedback passive controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. The existence conditions of the controller can be expressed by linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the feasibility and effectiveness of the proposed method.

A Novel Approach to Filter Design for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay

In this paper, the problem of l2- l∞ filtering for a class of discrete-time Takagi-Sugeno (T-S) fuzzy time-varying delay systems is studied. Our attention is focused on the design of full- and reduced-order filters that guarantee the filtering error system to be asymptotically stable with a prescribed H∞ performance. Sufficient conditions for the obtained filtering error system are proposed by applying an input-output approach and a two-term approximation method, which is employed to approximate the time-varying delay. The corresponding full- and reduced-order filter design is cast into a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, simulation examples are provided to illustrate the effectiveness of the proposed approaches.

Controller Design of Discrete-time Fuzzy Control Systems Based on Piecewise Lyapunov Function

Controller Design of Discrete-time Fuzzy Control Systems Based on Piecewise Lyapunov Function

Stability and Constrained Control of a Class of Discrete-Time Fuzzy Positive Systems with Time-Varying Delays

This paper deals with the stability of nonlinear discrete-time positive systems with time-varying delays represented by the Takagi–Sugeno (T–S) fuzzy model. The time-varying delays in the systems can be unbounded. Sufficient conditions of stability which are not relevant to the magnitude of delays are derived by a solution trajectory. Based on the stability results, the problems of controller design via the parallel distributed compensation (PDC) scheme are solved. The control is under the positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained control is also considered, further requiring that the state trajectory of the closed-loop system be bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results and control laws are formulated as linear matrix inequalities (LMIs) and linear programs (LPs). A numerical example and a real plant are studied to demonstrate the application of the proposed methods.

Distributed synchronization under uncertainty: A fuzzy approach

In this paper the synchronization of a network of identical systems with fuzzy initial conditions is introduced, as a convenient framework to obtain a shared estimation of the state of a system based on partial and distributed observations, in the case where such a state is affected by ambiguity and/or vagueness. After discussing the synchronization of crisp systems, providing a criteria to find the information sharing law that lets the network converge to a shared trajectory, Discrete-Time Fuzzy Systems (DFSs) are introduced as an extension of scalar fuzzy difference equations. Besides providing a stability condition for a general DFS, in the linear case it is proven that, under a non-negativity assumption for the coefficients of the system, the fuzzyfication of the initial conditions does not compromise the stability of the crisp system. A framework for the synchronization of arrays of linear DFS is then introduced, proving that the crisp synchronization is a particular case of the proposed approach. Finally, a case study in the field of Critical Infrastructure Protection is provided.

Fuzzy Control of a Class of Discrete-Time Fuzzy Bilinear Systems with Time-Delay

The stability control problem is considered for a class of discrete-time T-S fuzzy bilinear system with time-varying delay in both state and input. Based on the parallel distribute compensation (PDC) scheme, some sufficient conditions are derived to guarantee the global asymptotically stability of the overall fuzzy system, which are represented in terms of matrix inequality. The corresponding controller can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example shows that the approach is effective.