scholarly journals Synthesis of an LMI-based fuzzy control system with guaranteed cost performance: a piecewise Lyapunov approach

Author(s):  
Natache S. D. Arrifano ◽  
Vilma A. Oliveira ◽  
Lúcia V. Cossi

A new stability analysis and design of a fuzzy switching control based on uncertain Takagi-Sugeno fuzzy systems are proposed. The fuzzy system adopted is composed by a family of local linear uncertain systems with aggregation. The control design proposed uses local state feedback gains obtained from an optimization problem with guaranteed cost performance formulated in the context of linear matrix inequalities and a fuzzy switching scheme built from local Lyapunov functions. The global stability is guaranteed by considering a class of piecewise quadratic Lyapunov functions. Examples are given to illustrate the applicability of the proposed approach.

Author(s):  
Ibtissem Abdelmalek ◽  
Noureddine Goléa ◽  
Mohamed Hadjili

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy ModelsIn this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.


2020 ◽  
Vol 39 (3) ◽  
pp. 4147-4158
Author(s):  
Pedro H.S. Coutinho ◽  
Márcia L.C. Peixoto ◽  
Márcio J. Lacerda ◽  
Miguel Bernal ◽  
Reinaldo M. Palhares

This paper presents new stability and stabilisation conditions in the form of linear matrix inequalities for discrete-time Takagi-Sugeno fuzzy systems; they are derived considering a class of non-quadratic Lyapunov functions with multi-parametric non-monotonic terms, which significantly enhances the feasibility set of current state-of-the-art results. In addition, extensions to cope with the disturbance attenuation control problem are included. Benchmark numerical examples are provided to illustrate the effectiveness of the proposed approach.


Author(s):  
R. Sakthivel ◽  
P. Vadivel ◽  
K. Mathiyalagan ◽  
A. Arunkumar

This paper is concerned with the problem of robust reliable H∞ control for a class of uncertain Takagi-Sugeno (TS) fuzzy systems with actuator failures and time-varying delay. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance level. Based on the Lyapunov-Krasovskii functional (LKF) method together with linear matrix inequality (LMI) technique, a delay dependent sufficient condition is established in terms of LMIs for the existence of robust reliable H∞ controller. When these LMIs are feasible, a robust reliable H∞ controller can be obtained. Finally, two numerical examples with simulation result are utilized to illustrate the applicability and effectiveness of our obtained result.


2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yi-You Hou ◽  
Meei-Ling Hung ◽  
Jui-Sheng Lin

This paper investigates the guaranteed cost control of chaos problem in 4D Lorenz-Stenflo (LS) system via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the 4D Lorenz-Stenflo chaotic system. An illustrative example is provided to verify the validity of the results developed in this paper.


2020 ◽  
Vol 9 (3) ◽  
pp. 63-99
Author(s):  
Iqbal Ahammed A.K. ◽  
Mohammed Fazle Azeem

Most of the systems in the industry contain extreme non-linearity and uncertainties, which are hard to design and control utilizing general nonlinear systems. To conquer this sort of troubles, different plans have been produced in the most recent two decades, among which a popular methodology is Takagi-Sugeno fuzzy control. In this article, we present robust stabilization and control of Takagi-Sugeno (T-S) fuzzy systems with parameter uncertainties and disturbances. Initially, Takagi and Sugeno (TS) fuzzy model is used to represent a nonlinear system. Based on this T-S fuzzy model, fuzzy controller design schemes for state feedback and output feedback is also developed. Then, necessary conditions are derived for robust stabilization in the intelligence of Lyapunov asymptotic stability and are expressed in the arrangement of linear matrix inequalities (LMIs). The proposed system is implemented in the working platform of MATLAB and the simulation results are provided to illustrate the effectiveness of the proposed methods.


2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ken Yeh ◽  
Cheng-Wu Chen

The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist ofJinterconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.


2007 ◽  
Vol 16 (03) ◽  
pp. 545-552 ◽  
Author(s):  
CHENG-WU CHEN ◽  
CHEN-LIANG LIN ◽  
CHUNG-HUNG TSAI ◽  
CHEN-YUAN CHEN ◽  
KEN YEH

This study presents an H∞ controller design for time-delay T-S fuzzy systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The delay-dependent robust stability criterion is derived in terms of the fuzzy Lyapunov method to guarantee the stability of time-delay T-S fuzzy systems subjected to disturbances. Based on the delay-dependent condition and parallel distributed compensation (PDC) scheme, the controller design problem is transformed into solving linear matrix inequalities (LMI).


Author(s):  
Jun Yoneyama ◽  

A dynamical system is usually modeled as a continuous-time system, while the control input is applied at discrete instants. This is called a sampled-data control system. This paper is concerned with robust sampled-data control with guaranteed cost for uncertain fuzzy systems. The sampled-data control input is usually the zero-order hold and hence has a piecewise-continuous delay. Thus, an input delay system approach to robust sampled-data control is introduced. Sufficient robust guaranteed cost performance conditions for the closed-loop system with a sampled-data state feedback controller are given in terms of linear matrix inequalities(LMIs). Such robust conditions are derived via descriptor approach to fuzzy time-delay systems under the assumption that a sampling interval may vary but is not greater than some prescribed number. A design method of robust sampled-data guaranteed cost controller for uncertain fuzzy systems. Numerical examples are given to illustrate our sampled-data state feedback control.


2014 ◽  
Vol 536-537 ◽  
pp. 1187-1190
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang

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.


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