Improving the stability conditions of TS fuzzy systems with fuzzy Lyapunov functions

In this paper, the fuzzy Lyapunov function approach is considered for stabilizing continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing a slack LMI variable into the problem formulation. The stability results are thus used in the state feedback design which is also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilizing conditions presented. © 2011 IFAC.

Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented. © 2013 Copyright Taylor and Francis Group, LLC.

A fuzzy Lyapunov function approach for stabilization and control of switched TS fuzzy systems

In this work, sufficient conditions for the existence of switching laws for stabilizing switched TS fuzzy systems via a fuzzy Lyapunov function are proposed. The conditions are found by exploring properties of the membership functions and are formulated in terms of linear matrix inequalities (LMIs). Stabilizing switching conditions with bounds on the decay rate solution and H1 performance are also obtained. Numerical examples illustrate the effectiveness of the proposed design methods.

TS-fuzzy controlled DFIG based wind energy conversion system

This paper focuses on the implementation of the TS (Tagaki-Sugino) fuzzy controller for the active power and the DC capacitor voltage control of the Doubly Fed Induction Generator (DFIG) based wind generator. DFIG system is represented by a third-order model where electromagnetic transients of the stator are neglected. The effectiveness of the TS-fuzzy controller on the rotor speed oscillations and the DC capacitor voltage variations of the DFIG damping controller on converter ratings of the DFIG system is also investigated. The results of the time domain simulation studies are presented to elucidate the effectiveness of the TS-fuzzy controller compared with conventional PI controller in the DFIG system. The proposed TS-fuzzy controller can improve the fault ride through capability of DFIG compared to the conventional PI controller

Análise da estabilidade de sistemas fuzzy Takagi-Sugeno utilizando as desigualdades de Lyapunov-Metzler

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Novas condições de estabilidade de sistemas não lineares utilizando funções de Lyapunov fuzzy

Pós-graduação em Engenharia Elétrica - FEIS

Application of TS-Fuzzy Controller for Active Power and DC Capacitor Voltage Control in DFIG-Based Wind Energy Conversion Systems

This chapter focuses on the implementation of the TS (Tagaki-Sugino) fuzzy controller for the Doubly Fed Induction Generator (DFIG) based wind generator. The conventional PI control loops for mantaining desired active power and DC capacitor voltage is compared with the TS fuzzy controllers. DFIG system is represented by a third-order model where electromagnetic transients of the stator are neglected. The effectiveness of the TS-fuzzy controller on the rotor speed oscillations and the DC capacitor voltage variations of the DFIG damping controller on converter ratings is also investigated. The results from the time domain simulations are presented to elucidate the effectiveness of the TS-fuzzy controller over the conventional PI controller in the DFIG system. The proposed TS-fuzzy con-troller can improve the fault ride through capability of DFIG compared to the conventional PI controller.

Optimization of gaussian fuzzy membership functions and evaluation of the monotonicity property of fuzzy inference systems

In this paper, two issues relating to modeling of a monotonicity-preserving Fuzzy Inference System (FIS) are examined. The first is on designing or tuning of Gaussian Membership Functions (MFs) for a monotonic FIS. Designing Gaussian MFs for an FIS is difficult because of its spreading and curvature characteristics. In this study, the sufficient conditions are exploited, and the procedure of designing Gaussian MFs is formulated as a constrained optimization problem. The second issue is on the testing procedure for a monotonic FIS. As such, a testing procedure for a monotonic FIS model is proposed. Applicability of the proposed approach is demonstrated with a real world industrial application, i.e., Failure Mode and Effect Analysis. The results obtained are analysis and discussed. The outcomes show that the proposed approach is useful in designing a monotonicity-preserving FIS model.

Estimating fuzzy membership functions parameters by the levenberg-marquardt algorithm

In previous papers from the authors fuzzy model identification methods were discussed. The bacterial algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg-Marquardt algorithm was also proposed for determining membership functions in fuzzy systems. In this paper the Levenberg-Marquardt technique is improved to optimise the membership functions in the fuzzy rules without Ruspini-partition. The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear functions as well.

Fuzzy Membership Functions in a Fuzzy Decision Making Problem

Authors analyses questions of the subjective uncertainty and inexactness situations in the moment of using expert information and another questions which are connected with expert information uncertainty by fuzzy sets with rough membership functions in this article. You can find information about integral problems of individual expert marks and about connection among total marks “degree of inexactness” with sensibility of measurement scale. A lot of different situation which are connected with distribution of the function accessory significance and orientation of the concrete take to task decision making are analyses here.

Quadratic Lyapunov functions for linear systems Journal

The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation S0305004100044777_inline1 The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable sy

Stability of time-delay systems via Lyapunov functions

In this paper, a Lyapunov function candidate is introduced for multivariable systems with inner delays, without assuming a priori stability for the nondelayed subsystem. By using this Lyapunov function, a controller is deduced. Such a controller utilizes an input-output description of the original system, a circumstance that facilitates practical applications of the proposed approach.

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)