scholarly journals LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms

2014 ◽  
Vol 24 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Observer Design ◽  
System Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Observer ◽  
Quadratic Inequalities ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

Abstract The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.

scholarly journals Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Chang Che ◽  
Jiayao Peng ◽  
Tao Zhao ◽  
Jian Xiao ◽  
Jie Zhou
Keyword(s):  
Nonlinear Systems ◽  
Integral Inequality ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
State Delays ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S) fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs) are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

Admissible Conditions for T-S Fuzzy Descriptor Systems with Non-Differentiable Membership Functions

2013 ◽  
Vol 415 ◽  
pp. 259-266
Author(s):  
Peng Lin ◽  
Gang Hu
Keyword(s):  
Continuous Time ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Structural Information ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Membership Functions ◽  
Matrix Inequalities ◽  
Closed Loop Systems ◽  
Takagi Sugeno

In this paper, the admissible conditions (regular, impulse-free and stable) for a class of continuous-time Takagi-Sugeno (T-S) fuzzy descriptor systems are investigated. Sufficient admissible conditions for the closed-loop systems under non-parallel distributed compensation (non-PDC) feedback are proposed. This approach is mainly based on the state space division properly to make the membership functions continuous differentiable. Moreover, in order to make good use of the systems’ structural information in rules, the provided conditions are obtained through fuzzy Lyapunov functions candidate and can be formulated in terms of dilated Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed approach is shown through numerical example by using the optimization toolbox.

scholarly journals Stable Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi–Sugeno (T–S) fuzzy models. Takagi–Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T–S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T–S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi–Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T–S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

A Simple, Natural and Effective Framework of Nonlinear Systems Control and its Application to Aerial Robots

2014 ◽  
Vol 26 (2) ◽  
pp. 140-147 ◽  
Author(s):  
Motoyasu Tanaka ◽  
◽  
Hiroshi Ohtake ◽  
Kazuo Tanaka ◽  
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Design Problems ◽  
Model Based Control ◽  
Aerial Robots ◽  
Control Framework ◽  
Systems Control ◽  
Takagi Sugeno

This paper presents a simple, natural and effective framework of nonlinear systems control and its application to aerial robots. First, we present a framework of Takagi-Sugeno fuzzy model-based control and also discuss its feature. Next, a number of design problems for the control framework are formulated as numerically feasibility problems of representing in terms of linear matrix inequalities. Finally, we provide two applications of the control framework to aerial robots. The control results of aerial robots show the utility of the control framework.

scholarly journals Stabilizing Fuzzy Output Control for a Class of Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Design Procedure ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Output Control ◽  
Output Controller ◽  
Control Scheme ◽  
Lyapunov Matrix ◽  
Takagi Sugeno

The paper presents new conditions suitable in design of a stabilizing output controller for a class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the fuzzy control scheme relating to the parallel distributed output compensators, the sufficient design conditions are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and guarantees global stability of the system. Simulation result illustrates the design procedure and demonstrates the performances of the proposed design method.

Finite-Frequency Static Output Feedback H∞ Control of Continuous-Time T–S Fuzzy Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Redouane Chaibi ◽  
Ismail Er Rachid ◽  
El Houssaine Tissir ◽  
Abdelaziz Hmamed
Keyword(s):  
Output Feedback ◽  
Continuous Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Takagi Sugeno ◽  
Static Output

This paper is concerned with finite-frequency static output feedback (SOF) [Formula: see text] control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy systems. With the aid of the generalized Kalman–Yakubovich–Popov (GKYP) lemma, sufficient conditions for the existence of the finite-frequency SOF [Formula: see text] control are presented. The bilinear matrix inequalities are converted to a set of linear matrix inequalities, with the aid of some special derivations. Two practical examples are given to demonstrate the effectiveness of the proposed method.

scholarly journals State and fault estimation based on fuzzy observer for a class of Takagi-Sugeno singular models

2022 ◽  
Vol 25 (1) ◽  
pp. 172
Author(s):  
Kaoutar Ouarid ◽  
Mohamed Essabre ◽  
Abdellatif El Assoudi ◽  
El Hassane El Yaagoubi
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Theory ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Engineering Practice ◽  
Sensor Faults ◽  
Matrix Inequalities ◽  
Decomposition Approach ◽  
New Approach ◽  
Takagi Sugeno

Singular nonlinear systems have received wide attention in recent years, and can be found in various applications of engineering practice. On the basis of the Takagi-Sugeno (T-S) formalism, which represents a powerful tool allowing the study and the treatment of nonlinear systems, many control and diagnostic problems have been treated in the literature. In this work, we aim to present a new approach making it possible to estimate simultaneously both non-measurable states and unknown faults in the actuators and sensors for a class of continuous-time Takagi-Sugeno singular model (CTSSM). Firstly, the considered class of CTSSM is represented in the case of premise variables which are non-measurable, and is subjected to actuator and sensor faults. Secondly, the suggested observer is synthesized based on the decomposition approach. Next, the observer’s gain matrices are determined using the Lyapunov theory and the constraints are defined as linear matrix inequalities (LMIs). Finally, a numerical simulation on an application example is given to demonstrate the usefulness and the good performance of the proposed dynamic system.

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