Discrete-time Takagi-Sugeno Fuzzy Systems Research Articles

Analysis and Design of Robust H∞ Fault Estimation Observer With Finite-Frequency Specifications for Discrete-Time Fuzzy Systems.

This paper addresses the problem of fault estimation observer design with finite-frequency specifications for discrete-time Takagi-Sugeno (T-S) fuzzy systems. First, for such T-S fuzzy models, an H∞ fault estimation observer with pole-placement constraint is proposed to achieve fault estimation. Based on the generalized Kalman-Yakubovich-Popov lemma, the given finite-frequency observer possesses less conservatism compared with the design of the entire-frequency domain. Furthermore, the performance of the presented fault estimation observer is further enhanced by adding the degree of freedom. Finally, two examples are presented to illustrate the effectiveness of the proposed strategy.

State Estimation of Discrete-Time Takagi-Sugeno Fuzzy Systems in a Network Environment.

In this paper, we investigate the H∞ filtering problem of discrete-time Takagi'Sugeno (T-S) fuzzy systems in a network environment. Different from the well used assumption that the normalized fuzzy weighting function for each subsystem is available at the filter node, we consider a practical case in which not only the measurement but also the premise variables are transmitted via the network medium to the filter node. For the network characteristics, we consider the multiple packet dropouts which are described by using a Markov chain. It is assumed that the filter uses the most recent packet. If there are packet dropouts occurring, the filter adopts the information for the last received packet. Suppose that the mode of the Markov chain is ordered according to the number of consecutive packet dropouts from zero to a preknown maximal value. For each mode of the Markov chain, it only has at most two jumping actions: 1) jump to the first mode and the current packet is transmitted successfully and 2) jump to the next mode and the number of consecutive packet dropouts increases by one. We aim to design mode-dependent and fuzzy-basis-dependent T-S fuzzy filter by using the transmitted packet subject to the described network issue. With the augmentation technique, we obtain a stochastic filtering error system in which the filter parameters and the Markovian jumping variable are all involved. A sufficient condition which guarantees the stochastic stability and the H∞ performance is derived with the Lyapunov method. Based on the sufficient condition, we propose the filter design method and the filter parameters can be determined by solving a set of linear matrix inequalities (LMIs). A tunnel-diode circuit in a network environment is presented to show the effectiveness and the advantage of the proposed design approach.

Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach.

This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Stability of a Class of Discrete-Time Switched Fuzzy Systems by Arbitrary Switching

This paper investigates a representation model, namely, a discrete-time switched fuzzy system. In this model, a system is a switched system whose subsystems are all discrete-time Takagi-Sugeno (T-S) fuzzy systems. For the proposed discrete-time switched fuzzy system is built to ensure that the relevant system is asymptotically stable by Arbitrary Switching and the Lyapunov functions method. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.

Dissipativity Analysis and Synthesis for Discrete-Time T–S Fuzzy Stochastic SystemsWith Time-Varying Delay

This paper is concerned with the problems of dissipativity analysis and synthesis for discrete-time Takagi-Sugeno fuzzy systems with stochastic perturbation and time-varying delay. First, a novel model transformation method is introduced to pull the time-varying delay uncertainty out of the original system. Consequently, the transformed model is composed of a linear time-invariant system and a norm-bounded uncertain subsystem. By using this model transformation method combined with the Lyapunov-Krasovskii technique, sufficient conditions of the dissipativity are established. Then, a fuzzy controller is designed to guarantee the dissipative performance of the closed-loop system. Finally, three examples are presented: one shows the effectiveness of model transformation method, the second performs the comparison with alternative approaches, and the third illustrates the applicability of the proposed dissipative control methods.

Relaxed observer design of discrete-time T–S fuzzy systems via a novel multi-instant fuzzy observer

This paper is concerned with the design of observer for discrete-time Takagi–Sugeno fuzzy systems. Under the framework of multi-instant matrix, a novel fuzzy observer and a new Lyapunov function, which are parameter-dependent on m-steps normalized fuzzy weighting functions, are proposed for conceiving less conservative observer design conditions. In particular, some existing fuzzy Lyapunov functions and fuzzy observers are special cases of the new Lyapunov function and fuzzy observer, respectively. Furthermore, the obtained fuzzy observer design conditions are further relaxed by fully considering the algebraic properties of m-steps normalized fuzzy weighting functions. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

Stability and Stabilization of Discrete-Time T–S Fuzzy Systems With Stochastic Perturbation and Time-Varying Delay

This paper is concerned with the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation and time-varying state delay. By means of the delay-partitioning method and slack variables, a novel fuzzy Lyapunov-Krasovskii function is constructed to reduce the conservatism of stability conditions. Those conditions are converted to finite linear matrix inequalities, which can be readily solved by standard numerical software. Then, the delay-dependent stabilization approach, which is based on a nonparallel distributed compensation scheme, is introduced for the closed-loop fuzzy systems. Finally, illustrative examples are provided to illustrate the feasibility and effectiveness of the proposed methods.

Fuzzy Filtering With Randomly Occurring Parameter Uncertainties, Interval Delays, and Channel Fadings

In this paper, the H∞ fuzzy filtering problem is investigated for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with randomly occurring uncertainties and randomly occurring interval time-varying delays, as well as channel fadings. A sequence of random variables obeying the Bernoulli distribution is utilized to govern the randomly occurring uncertainties and probabilistic interval time-varying delays. Simultaneously, the Rice fading model is employed to describe the phenomena of channel fadings by setting different values of the channel coefficients. Our attention is focused on the design of an H∞ fuzzy filter such that the filtering error dynamics is exponentially mean-square stable and the disturbance rejection attenuation is constrained to a given level by means of the H∞-performance index. In the presence of the randomly occurring phenomena, sufficient conditions are derived, via stochastic analysis and Lyapunov functional approach, for the existence of desired filter ensuring both the exponential mean-square stability and the prescribed H∞ performance. The filter parameters can be obtained by solving a convex optimization problem via the semidefinite program method. Finally, a numerical example is utilized to illustrate the usefulness and effectiveness of the proposed design technique.

A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays

This paper focuses on analyzing a new model transformation of discrete-time Takagi–Sugeno (T–S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new comparison model is proposed by employing a new approximation for time-varying delay state, and then, a delay partitioning method is used to analyze the scaled small gain of this comparison model. A sufficient condition on discrete-time T–S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\ell_{2}$</tex></formula> disturbance attenuation performance, is derived by employing the scaled small-gain theorem. Then, the solvability condition for the induced <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\ell_{2}$</tex></formula> DOF control is also established, by which the DOF controller can be solved as linear matrix inequality optimization problems. Finally, examples are provided to illustrate the effectiveness of the proposed approaches.

Linear matrix inequality approach to local stability analysis of discrete‐time Takagi–Sugeno fuzzy systems

This study deals with the problem of local stability analysis and the computation of invariant subsets of the domain of attraction (DA) for discrete-time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions, new sufficient conditions and an iterative scheme are proposed in order to prove the local stability and to estimate the DA. The mean value theorem and polytopic type bounds on the gradient of the membership functions are used to consider the relation between the membership functions at samples k and k + 1. Each step of the iterative procedure consists of linear matrix inequalities (LMIs) or single-parameter minimisation problems subject to LMI constraints, which are solvable via convex optimisations. Finally, examples compare the proposed conditions with existing tests.

Optimal H∞-Based Linear-Quadratic Regulator Tracking Control for Discrete-Time Takagi–Sugeno Fuzzy Systems With Preview Actions

This paper investigates the optimal tracking control problem for discrete-time Takagi–Sugeno (T–S) systems. The control signal has three components: preview control for the previewable reference signal, integral control for the tracking error, and the state-feedback control for the plant. The optimization objective is a quadratic form of the tracking error and the control signal. By using the augmentation technique, the tracking controller design problem is converted into a design problem of the state-feedback controllers for augmented T–S fuzzy systems. The quadratic optimization objective is equivalent to the two-norm (in fact, the square of the two-norm) of a controlled output. Assuming that the external inputs of the augmented systems are l2 bounded, the H∞ performance index is employed to investigate and optimize the controller design. The controller gains can be obtained by solving a sequence of linear matrix inequalities (LMIs). An example on electromechanical system shows the efficacy of the proposed design method.

Formula omitted] fault detection filter design for discrete-time Takagi–Sugeno fuzzy system

In this note, a robust fault detection observer is designed for a T–S (Takagi–Sugeno) fuzzy model with sensor faults and unknown bounded disturbances. The method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable. The idea is to formulate the robust fault detection observer design as an H−/H∞ problem. Based on nonquadratic Lyapunov functions, a solution of the considered problem is then given via a Linear Matrix Inequality (LMI) formulation. An example is proposed to illustrate the design conditions.

Reduced-order ℓ2-ℓ∞ filtering for discrete-time T-S fuzzy systems with stochastic perturbation

This paper is concerned with the problem of ℓ2-ℓ∞ filtering for discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation. Firstly, a basis-dependent existence condition of desirable ℓ2-ℓ∞ filters is proposed. Then by means of the convex linearisation technique, the derived condition is transformed into some strict linear matrix inequality (LMI) constraints, by which both full- and reduced-order filters can be designed. Moreover, for the reduced-order ℓ2-ℓ∞ filter design, a novel analysis and design method with the projection lemma is also provided. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the proposed full- and reduced-order ℓ2-ℓ∞ filter design methods.

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.

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.

Actuator Saturation Constrained Fuzzy Control for Discrete Stochastic Fuzzy Systems with Multiplicative Noises

This paper deals with the fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with multiplicative noises. Using the Lyapunov stability theory and It&#xf4; formula, the sufficient conditions are derived to guarantee the stability of the closed-loop nonlinear stochastic systems subject to actuator saturation. Based on the Parallel Distributed Compensation (PDC) concept, the fuzzy controller can be obtained to stabilize the T-S fuzzy models with multiplicative noises by combining the same membership functions of plants and desired state feedback gains. In order to illustrate the availability and practicability of proposed fuzzy controller design approach, the numerical simulations for the nonlinear truck-trailer system are given to demonstrate the applications of this paper.

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.

LMI Solution for Robust Static Output Feedback Control of Discrete Takagi–Sugeno Fuzzy Models

This paper deals with the stabilization problem of discrete-time Takagi-Sugeno (T-S) fuzzy systems via static output controller (SOFC). The proposed method uses the descriptor approach to study this problem and leads to strict linear matrix inequality ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LMI</i> ) formulation. In contrast with the existing results, the method allows coping with multiple output matrices, as well as uncertainties. Moreover, the new proposed method can lead to less conservative results by introducing slack variables and considering multiple Lyapunov matrices. A robust SOFC for uncertain T-S fuzzy models is also derived in strict <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LMI</i> terms. Numerical examples are given to illustrate the effectiveness of the proposed design results.

Robust stabilization of state delayed discrete-time Takagi—Sugeno fuzzy systems with input saturation via an anti-windup fuzzy design

We consider the robust stabilization problem for discrete-time Takagi—Sugeno (T—S) fuzzy systems with time-varied delays subjected to input saturation. We design static and dynamic anti-windup fuzzy controllers to ensure the convergence of all admissible initial states within the domain of attraction. Based on the project lemma and classical sector conditions, the conditions for the existence of solutions to this problem are obtained and expressed in terms of a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.

Special issue on ‘new results on neuro‐fuzzy adaptive control systems’

Special issue on ‘new results on neuro‐fuzzy adaptive control systems’