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.

scholarly journals A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

2007 ◽  
Vol 17 (1) ◽  
pp. 39-51 ◽  
Author(s):  
Ibtissem Abdelmalek ◽  
Noureddine Goléa ◽  
Mohamed Hadjili
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
Time Derivative ◽  
Stability Conditions ◽  
Membership Functions ◽  
Lyapunov Approach ◽  
Fuzzy Models ◽  
Quadratic Stabilization ◽  
Quadratic Lyapunov Functions ◽  
Takagi Sugeno

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.

Improved Delay-Dependent Stability of Nonlinear Quadratic TS Fuzzy Systems

2019 ◽  
Vol 29 (09) ◽  
pp. 2050134 ◽  
Author(s):  
Khadija Naamane ◽  
El Houssaine Tissir
Keyword(s):  
Fuzzy Systems ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper focuses on the problem of delay-dependent stability for nonlinear quadratic Takagi–Sugeno (TS) fuzzy systems with time-varying delay using the input–output approach. The results are based on the model transformation by employing a three-terms approximation of delayed state vector. By applying the scaled small-gain theorem and Lyapunov–Krasovskii functional, the stability criteria is obtained in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, the numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous work.

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 Controllers Design based on Takagi-Sugeno Fuzzy Systems and Sliding Mode for a Non-Holonomic Mobile robot

2021 ◽  
Author(s):  
hafedh Abid
Keyword(s):  
Mobile Robot ◽  
Fuzzy Systems ◽  
Sliding Mode ◽  
Control Laws ◽  
Kinematic Behavior ◽  
Integral Controller ◽  
Proportional Integral Controller ◽  
The Stability ◽  
Takagi Sugeno ◽  
Holonomic Mobile Robot

Abstract This paper is interesting to a nonholonomic wheeled mobile robot. We have presented a scheme to develop controllers. Two controllers have been developed. The first concerns the kinematic behavior while the second relates to the dynamic behavior of the mobile robot. For the Kinematic controller, we have used a Takagi-Sugeno fuzzy system to overcome the nonlinearities present in model whereas for the second controller we have used the sliding mode approach. The sliding surface has the identical structure as the proportional integral controller. The stability of system has been proved based on Lyapunov approach. The simulation results show the efficiency of the proposed control laws.

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.

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

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.

A Gain-Scheduling Control Approach for Takagi–Sugeno Fuzzy Systems Based on Linear Parameter-Varying Control Theory

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Yang Liu ◽  
Xiaojun Ban ◽  
Fen Wu ◽  
H. K. Lam
Keyword(s):  
Fuzzy Control ◽  
Control Theory ◽  
Fuzzy Systems ◽  
Gain Scheduling ◽  
Control Problems ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Fuzzy Models ◽  
Gain Scheduling Control ◽  
Takagi Sugeno

Due to the universal approximation capability of Takagi–Sugeno (T–S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T–S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T–S fuzzy models and LPV models provides a new perspective of the control problems for T–S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gain-scheduling control design approach for T–S fuzzy systems is presented to ensure globally asymptotical stability and optimize H∞ performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.

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