On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems

2014 ◽  
Vol 351 (7) ◽  
pp. 3707-3718 ◽  
Author(s):  
Fernando O. Souza ◽  
Víctor C.S. Campos ◽  
Reinaldo M. Palhares
Keyword(s):  
Fuzzy Systems ◽  
Stability Conditions ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Delay Dependent Stability

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.

New Approach to Non-Fragile Control of Uncertain Fuzzy Systems with Time-Delay

2013 ◽  
Vol 433-435 ◽  
pp. 1131-1135
Author(s):  
Li Li
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
Time Delays ◽  
Upper Bounds ◽  
Stability Conditions ◽  
New Approach ◽  
State And Input Delays ◽  
Input Delays ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper focuses on the delay-dependent stability analysis and stabilization for T-S fuzzy system systems with state and input delays. Some new and less conservative delay-dependent small stability conditions are explicitly obtained. The upper bounds of time-delays are obtained by using small convex optimization.Finally, a numerical example is included to show the effectiveness.

On delay-dependent stability conditions

2000 ◽  
Vol 40 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Vladimir L. Kharitonov ◽  
Daniel Melchor-Aguilar
Keyword(s):  
Stability Conditions ◽  
Delay Dependent ◽  
Delay Dependent Stability

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.

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