Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed

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A Survey on Analysis and Design of Model-Based Fuzzy Control Systems

New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI

This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in linear matrix inequality (LMI) terms. Both continuous-time and discrete-time cases are studied. Relaxations are introduced by using intermediate variables. Extension to the case of unmeasured decision variables is also given. A numerical example is given to illustrate the effectiveness of the given results.

Robust Observer Design for Unknown Inputs Takagi–Sugeno Models

We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.

Observers for Takagi-Sugeno fuzzy systems

This paper is concerned with the network-based robust fault detection problem for a class of uncertain discrete-time Takagi-Sugeno fuzzy systems with stochastic mixed time delays and successive packet dropouts. The mixed time delays comprise both the multiple discrete time delays and the infinite distributed delays. A sequence of stochastic variables is introduced to govern the random occurrences of the discrete time delays, distributed time delays, and successive packet dropouts, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fuzzy fault detection filter such that the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fuzzy fault detection filters, and then, the corresponding solvability conditions for the desired filter gains are established. In addition, the optimal performance index for the addressed robust fuzzy fault detection problem is obtained by solving an auxiliary convex optimization problem. An illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

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Fuzzy-Model-Based Robust Fault Detection With Stochastic Mixed Time Delays and Successive Packet Dropouts

We consider the analysis and design of three different types of nonlinear observers for dynamic Takagi-Sugeno fuzzy systems. Our approach is based on extending existing nonlinear observer schemes, namely Thau-Luenberger and sliding mode observers, to the case of interpolated multiple local affine linear models. Then linear matrix inequality based techniques are used for observer analysis and design.

Fuzzy observers

Deals with local fuzzy Thau-Luenberger observers for nonlinear plants. A nonlinear plant is approximated by a Takagi-Sugeno (TS) fuzzy multiple model with affine subsystems for which local linear fuzzy observers are constructed. Analysis of stability conditions for the complete observer is made and a design procedure based on linear matrix inequalities is devised. A simulation example is also given for an open loop model.

Thau-Luenberger observers for TS fuzzy systems

Deals with a sliding mode fuzzy observer for nonlinear plants. A nonlinear plant is approximated by a multiple model Takagi Sugeno (TS) fuzzy system and then transformed into a canonical form for which a nonlinear observer is constructed. The paper presents a type of sliding mode fuzzy observer that deals with matched and unmatched uncertainties in the plant model very effectively.

P. Bergsten

Papers

Observers for Takagi-Sugeno fuzzy systems

Fuzzy observers

Thau-Luenberger observers for TS fuzzy systems

Sliding mode observer for a Takagi Sugeno fuzzy system