On the stability issues of linear Takagi-Sugeno fuzzy models

1998 ◽  
Vol 6 (3) ◽  
pp. 402-410 ◽  
Author(s):  
Joongseon Joh ◽  
Ye-Haw Chen ◽  
R. Langari
Keyword(s):  
Fuzzy Models ◽  
The Stability ◽  
Stability Issues ◽  
Takagi Sugeno

STABILITY ANALYSIS OF NONLINEAR INTERCONNECTED SYSTEMS VIA T–S FUZZY MODELS

2004 ◽  
Vol 04 (01) ◽  
pp. 41-55 ◽  
Author(s):  
WEI-LING CHIANG ◽  
CHENG-WU CHEN ◽  
FENG-HSIAG HSIAO
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Fuzzy Models ◽  
Fuzzy Techniques ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability problem of nonlinear interconnected systems. Each of them consists of a few interconnected subsystems which are approximated by Takagi–Sugeno (T–S) type fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of interconnected systems. It is shown that the stability analysis problems of nonlinear interconnected systems can be reduced to linear matrix inequality (LMI) problems via suitable Lyapunov functions and T–S fuzzy techniques. Finally, numerical examples with simulations are given to demonstrate the validity of the proposed approach.

scholarly journals T-S Fuzzy Model Based Control Strategy for the Networked Suspension Control System of Maglev Train

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Guang He ◽  
Jie Li ◽  
Peng Cui ◽  
Yun Li
Keyword(s):  
Control System ◽  
Control Strategy ◽  
State Feedback ◽  
Fuzzy Model ◽  
Maglev Train ◽  
Fuzzy Models ◽  
Physical Experiments ◽  
Suspension Control ◽  
The Stability ◽  
Takagi Sugeno

The control problem for the networked suspension control system of maglev train with random induced time delay and packet dropouts is investigated. First, Takagi-Sugeno (T-S) fuzzy models are utilized to represent the discrete-time nonlinear networked suspension control system, and the parameters uncertainties of the nonlinear model have also been taken into account. The controllers take the form of parallel distributed compensation. Then, a sufficient condition for the stability of the networked suspension control system is derived. Based on the criteria, the state feedback fuzzy controllers are obtained, and the controller gains can be computed by using MATLAB LMI Toolbox directly. Finally, both the numerical simulations and physical experiments on the full-scale single bogie of CMS-04 maglev train have been accomplished to demonstrate the effectiveness of this proposed method.

scholarly journals Improved T-S Fuzzy Control for Uncertain Time-Delay Coronary Artery System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zhenyu Zhu ◽  
Zhanshan Zhao ◽  
Haoliang Cui ◽  
Fengdong Shi
Keyword(s):  
Coronary Artery ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Practical Significance ◽  
Linear Matrix ◽  
System State ◽  
Fuzzy Models ◽  
The Stability ◽  
Uncertain Time ◽  
Takagi Sugeno

This paper is based on the Takagi-Sugeno (T-S) fuzzy models to construct a coronary artery system (CAS) T-S fuzzy controller and considers the uncertainties of system state parameters in CAS. We propose the fuzzy model of CAS with uncertainties. By using T-S fuzzy model of CAS and the use of parallel distributed compensation (PDC) concept, the same fuzzy set is assigned to T-S fuzzy controller. Based on this, a PDC controller whose fuzzy rules correspond to the fuzzy model is designed. By constructing a suitable Lyapunov-Krasovskii function (LKF), the stability conditions of the linear matrix inequality (LMI) are exported. Simulation results show that the method proposed in this paper is correct and effective and has certain practical significance.

scholarly journals Control of a hydraulic system by means of a fuzzy approach

2013 ◽  
Vol 3 (2) ◽  
pp. 121-131 ◽  
Author(s):  
Mohamed Ksantini ◽  
Ameni Ellouze ◽  
Francois Delmotte
Keyword(s):  
Hydraulic System ◽  
Closed Loop ◽  
Linear Models ◽  
Linear Functions ◽  
Control Law ◽  
Lyapunov Approach ◽  
Fuzzy Models ◽  
Non Linear ◽  
The Stability ◽  
Takagi Sugeno

Non linear models can be represented conveniently by Takagi-Sugeno fuzzy models when nonlinearities are bounded. This approach uses a collection of linear models which are interpolated by non linear functions. Then the global control law is the interpolation by the same functions of each feedback associated to each linear model. A Lyapunov approach enables to compute these feedback gains. The number of linear models depends directly on the number of nonlinearities the system has. The more models there are, the more difficult it is to guarantee the stability of the closed loop. This paper proposes a method to reduce the number of linear models by assuming a number of nonlinearities considered as uncertainties and to guarantee the global exponential stability of the system. This method is applied on a hydraulic system.

scholarly journals Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3129
Author(s):  
Ameni Ellouze ◽  
Omar Kahouli ◽  
Mohamed Ksantini ◽  
Ali Rebhi ◽  
Nidhal Hnaien ◽  
...  
Keyword(s):  
Fuzzy Systems ◽  
Discrete Systems ◽  
Continuous Systems ◽  
Fuzzy Models ◽  
Discrete Approach ◽  
Quadratic Lyapunov Functions ◽  
The Stability ◽  
Takagi Sugeno ◽  
Stability Results ◽  
Discrete Controller

Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology.

Determining the Norton’s Equivalent Model of Distribution System with Distributed Generation (DG) for Stability Analysis

2019 ◽  
Vol 12 (2) ◽  
pp. 190-198
Author(s):  
Sunny Katyara ◽  
Lukasz Staszewski ◽  
Faheem Akhtar Chachar
Keyword(s):  
Distributed Generation ◽  
Normal Condition ◽  
Distribution System ◽  
Distribution Networks ◽  
Equivalent Model ◽  
Stability Factor ◽  
Matlab Simulation ◽  
The Stability ◽  
Stability Issues

Background: Since the distribution networks are passive until Distributed Generation (DG) is not being installed into them, the stability issues occur in the distribution system after the integration of DG. Methods: In order to assure the simplicity during the calculations, many approximations have been proposed for finding the system’s parameters i.e. Voltage, active and reactive powers and load angle, more efficiently and accurately. This research presents an algorithm for finding the Norton’s equivalent model of distribution system with DG, considering from receiving end. Norton’s model of distribution system can be determined either from its complete configuration or through an algorithm using system’s voltage and current profiles. The algorithm involves the determination of derivative of apparent power against the current (dS/dIL) of the system. Results: This work also verifies the accuracy of proposed algorithm according to the relative variations in the phase angle of system’s impedance. This research also considers the varying states of distribution system due to switching in and out of DG and therefore Norton’s model needs to be updated accordingly. Conclusion: The efficacy of the proposed algorithm is verified through MATLAB simulation results under two scenarios, (i) normal condition and (ii) faulty condition. During normal condition, the stability factor near to 1 and change in dS/dIL was near to 0 while during fault condition, the stability factor was higher than 1 and the value of dS/dIL was away from 0.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

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