This paper presents new relaxed stability conditions and LMI- (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented by Takagi-Sugeno's (TS) fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the TS fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers, LMI-based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. Other LMI's with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI-based design procedures.

Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs

This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems, First, a stability condition for Takagi and Sugeno's fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization, H/sup /spl infin// control theory, and linear matrix inequalities. The derived stability conditions are used to analyze the stability of Takagi and Sugeno's fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems, The design method employs the so-called parallel distributed compensation, important issues for the stability analysis and design are remarked. Finally, three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented.

Comments on "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H/sup /spl infin// control theory, and linear matrix inequalities"

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.

A multiple Lyapunov function approach to stabilization of fuzzy control systems

This paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of the separation property; that is, the fuzzy controller and the fuzzy observer can be independently designed. A numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer.

Analysis and design of fuzzy controller and fuzzy observer

The stability of a fuzzy feedback control system consisting of a fuzzy controller connected in series with a plant described by a fuzzy model is discussed. The stability analysis is based on some new theorems that guarantee sufficient conditions for asymptotical stability of the equilibrium point and total stability of the system. The stability analysis results are used to provide an approach to fuzzy controller design. The steps of the approach are specified through a design example.

Stability analysis and design of fuzzy control systems

Analysis and design of fuzzy control system

A pneumatic model-following control system using a fuzzy adaptive controller

In general, physical processes are usually nonlinear and control system design based on the linearization technique cannot control the process well for a wide range of operation. Use of the variable transformation method may not always solve the problem. In this paper, a fuzzy adaptive controller is proposed to control the nonlinear process. The CSTR control problem has also been considered. The results are compared with the method of nonlinear model predictive control (NMPC) with constrained and unconstrained control variables. A fuzzy model-following control system scheme is also proposed. The results show that the proposed controller is a feasible control structure for a nonlinear or parameter-variations process control.

Pey-Chung Chen

Papers

Analysis and design of fuzzy control system

A pneumatic model-following control system using a fuzzy adaptive controller

Application of fuzzy adaptive controller in nonlinear process control