Discrete Takagi-Sugeno Research Articles

Stabilization for a class of nonlinear systems: A fuzzy logic approach

In this paper, the problem of stabilization for the class of continuous time nonlinear systems which are discretized in closed form is addressed. By using the Takagi–Sugeno model approach, a discrete controller capable of stabilizing the discrete Takagi–Sugeno model and the continuous model as well, is obtained. This scheme allows using a digital controller for stabilizing an analog plant.

Control Law Proposition for the Stabilization of Discrete Takagi–Sugeno Models

This paper deals with the stabilization of a class of discrete nonlinear models, namely those in the Takagi-Sugeno form; its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate Lyapunov functions and an enhanced control law. It is shown that the use of the aforementioned Lyapunov function leads to less-pessimistic solutions. The usefulness of the new control law is shown through several examples.

A fault-tolerant control framework for a class of non-linear networked control systems

In this article, a novel fault-tolerant control (FTC) framework is presented for a class of non-linear networked control systems (NCSs) with Markov transfer delays. First, the NCSs are modelled by non-linear discrete Takagi–Sugeno fuzzy model using Euler approximate method. Then, a sliding mode-based fault estimation technique is developed for such model. With the estimated state and fault information, the proposed FTC framework can maintain the input-to-state stability of the faulty NCSs. A flexible joint robot link example is included to show the efficiency of the proposed method.

Discrete Takagi–Sugeno's Fuzzy Models: Reduction of the Number of LMI in Fuzzy Control Techniques

Conditions about the stabilization of Takagi-Sugeno fuzzy models can systematically be derived and solved usually using linear matrix inequality problems. Current research tries to lower any pessimism. However, often it leads to an important increase in the number of decision variables, and problems become unsolvable. In this correspondence, we choose to reduce the number of decision variables while not raising the conservatism in comparison with previous results. This correspondence deals with the discrete case, which is harder to solve. We supply results about the stabilization, the regulator problem, and also H( infinity) control.

Exponential stabilization for discrete Takagi–Sugeno fuzzy systems via impulsive control

This paper studies an impulsive control scheme for discrete Takagi–Sugeno (T–S) fuzzy systems. Some global exponential stability criteria are proposed in terms of linear matrix inequalities (LMIs), and based on which the procedure of impulsive controller design is proposed. A numerical example is included to illustrate the effectiveness of the proposed control scheme.

New Approaches to H∞ Controller Designs for Discrete T-S Fuzzy System

This paper proposed new approaches to stabilization analysis and H∞ performance for a class of discrete Takagi-Sugeno (T-S) fuzzy model. The main results given here concern their H∞ controllers design using PDC-like control laws and nonquadratic Lyapunov functions. New relaxed conditions and linear matrix inequality-based design methods are proposed that allow outperforming previous found in the literature. Finally, an example is given to demonstrate the efficiency of the proposed approaches.

A Sum of Squares Approach to Guaranteed Cost Control of Polynomial Discrete Fuzzy Systems

This paper presents a sum of squares (SOS) approach to guaranteed cost control of polynomial discrete fuzzy systems. First, we present a polynomial discrete fuzzy model that is more general representation of the well-known discrete Takagi-Sugeno (T-S) fuzzy model. Secondly, we derive a design condition based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the design approach discussed in this paper is more general than that based on the existing LMI approaches to discrete T-S fuzzy control system designs. The design condition realizes guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. A design example is provided to illustrate the validity of the design approach.

Decentralized state-feedback chaotification method of discrete Takagi–Sugeno fuzzy systems

A new chaotification method is proposed for making an arbitrarily given discrete Takagi–Sugeno (TS) fuzzy system chaotic. Based on a given discrete TS fuzzy system, the new chaotification method uses the decentralized state-feedback control and the continuous sawtooth function, instead of the modulo operation, to construct a chaotic nonlinear system, which can generate discrete chaos with the arbitrarily desired amplitude bound. We apply the improved Marotto theorem to mathematically prove that the controlled system is chaotic in the sense of Li and Yorke. In particular, an explicit formula for the computation of chaotification parameters is obtained. A numerical example is used to illustrate the theoretical results.

Discrete Fuzzy Controller Design for Achieving Common State Covariance Assignment

In this paper, a method is developed to find the output feedback fuzzy controllers for assigning a common state covariance matrix of discrete Takagi–Sugeno (T–S) fuzzy systems. The fuzzy control approach developed in this paper is based on the concept of Parallel Distributed Compensation (PDC). For each rule of the discrete T–S fuzzy model, it shows how to parameterize the static linear output feedback control gains to achieve a common state covariance matrix for each subsystem. Finally, a numerical example is provided to verify the effects of the proposed method.

Comments on “Constrained controller design of discrete Takagi–Sugeno fuzzy models”

In the above paper, Chang et al. (Fuzzy Sets and Systems 133 (2003) 37) proposed an interesting approach to design the fuzzy static output feedback controller with a common observability Gramian. However, since it involves a nonlinear output function, the results obtained are not correct for the general case. This note intends to circumvent these problems by modifying the approach proposed in Chang et al. (Fuzzy Sets and Systems 133 (2003) 37).

A projection scheme to stability analysis of discrete T–S fuzzy models

The paper deals with the stability analysis of the discrete Takagi–Sugeno’s (T–S) fuzzy model, which can describe a class of nonlinear systems. Based on the alternating projection method, the useful projection operators are derived firstly. And we thus proposed an efficient analysis algorithm for analyzing the stability. The effectiveness of the proposed method is illustrated by the numerical examples.

Constrained fuzzy controller design of discrete Takagi–Sugeno fuzzy models

The motivation for the work presented in this paper results from the need to find fuzzy controllers with a common observability Gramian for discrete Takagi–Sugeno fuzzy systems. The developed approach is based on the parallel distributed compensation concept. For each rule of the discrete Takagi–Sugeno fuzzy model, the present approach will show a way to parametrize the static linear output feedback control gains for achieving a certain common observability Gramian for all subsystems. A numerical example will be given to illustrate the utility of the proposed technique.

Anticontrol of chaos for discrete TS fuzzy systems

In this paper, a simple and systematic control design method is proposed for a discrete-time Takagi-Sugeno (TS) fuzzy system, which employs the parallel distributed compensation (PDC) to determine the structure of a fuzzy controller so as to make all the Lyapunov exponents of the controlled TS fuzzy system strictly positive. This approach is proven to be mathematically rigorous for anticontrol of chaos for a TS fuzzy system, in the sense that any given discrete-time TS fuzzy system can be made chaotic by the designed PDC controller along with the mod-operation. A numerical example is included to visualize the anticontrol effect.

Stability analysis of the discrete Takagi–Sugeno fuzzy model with time-varying consequent uncertainties

In this paper, we present two new robust stability criteria to analyze the robust stability of the discrete Takagi–Sugeno (TS) fuzzy dynamic model with time-varying consequent uncertainties. These proposed robust stability criteria do not need finding a common positive-definite matrix solution of Lyapunov equations and do not need solving any Lyapunov equation, therefore these robust stability criteria enable us to check the robust stability of the discrete TS fuzzy model with more convenient computation and enable us to analyze the robust stability of the discrete TS fuzzy model whose rules do not have a common positive-definite matrix solution of Lyapunov equations. Two examples are included to illustrate the applications of the proposed methods.

ON THE STABILITY OF DISCRETE TAKAGI-SUGENO FUZZY DYNAMIC MODEL

ABSTRACT In this paper, we present a new time domain stability criterion to analyze the stability of the discrete TS (Takagi-Sugeno) fuzzy dynamic model by which nonlinear systems can be precisely identified. Unlike recently reported sufficient stability criteria in which it is obligatory to find a common positive definite matrix solution of a set of Lyapunov equations, this proposed stability criterion does not require the solving of any Lyapunov equation. It is also not necessary to find a common positive definite matrix solution of a set of Lyapunov equations. Therefore, this stability criterion enables us to check the stability of the discrete TS fuzzy dynamic model with less computation. Two examples are included to illustrate the applications of the proposed method.