scholarly journals A reduction in conservatism in stability and 5 2 gain analysis of Takagi-Sugeno fuzzy systems via linear matrix inequalities

1999 ◽  
Vol 32 (2) ◽  
pp. 5451-5455 ◽  
Author(s):  
Ali Jadbabaie
Keyword(s):  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Takagi Sugeno

scholarly journals Finite frequency model reduction for 2-D fuzzy systems in FM model

2021 ◽  
Vol 297 ◽  
pp. 01035
Author(s):  
Rachid Naoual ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
State Space ◽  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Frequency Model ◽  
Takagi Sugeno

This paper deals with the problem of H∞ model reduction for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems described by Fornasini-Marchesini local state-space (FM LSS) models, over finite frequency (FF) domain. New design conditions guaranteeing the FF H∞ model reduction are established in terms of Linear Matrix Inequalities (LMIs). To highlight the effectiveness of the proposed H∞ model reduction design, a numerical example is given.

Robust H∞ Control for Takagi-Sugeno Fuzzy Systems with Time-Varying Delays in State and Input

2015 ◽  
Vol 764-765 ◽  
pp. 624-628 ◽  
Author(s):  
Shun Hung Tsai ◽  
Siou An Jian
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
State And Input Delays ◽  
Input Delays ◽  
Takagi Sugeno

In this paper, the robust H∞ stabilization problem for Takagi-Sugeno fuzzy control systemswith state and input delays is explored. Based on a Lyapunov-Krasoviskii function, the delaydependentstabilization conditions are proposed in terms of linear matrix inequalities (LMIs) to guaranteethe asymptotic stabilization of time-delay Takagi-Sugeno fuzzy systems with disturbance input.Finally, a numerical example is illustrated to demonstrate the feasibility and effectiveness of the proposed stabilization.

Stabilization of Nonlinear Systems Using Quasi-Linear Models

2000 ◽  
Author(s):  
Kiriakos Kiriakidis
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Models ◽  
Nonlinear Models ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Analysis And Design ◽  
Linear Differential Inclusions ◽  
Linear Differential ◽  
Generalized Lyapunov Functions ◽  
Takagi Sugeno

Abstract Unconventional nonlinear models such as nonlinear ARMAX, Takagi-Sugeno fuzzy models, global linearizations, and linear hybrid systems are, at the highest level of abstraction, a sort of quasi-linear models, namely, Polytopic Linear Differential Inclusions (PLDIs). At present, quadratic stability has enabled, mainly via linear matrix inequalities, the analysis and design of a nonlinear system from the vertex matrices of its PLDI model. Proving stability by a globally quadratic Lyapunov function, however, entails conservatism. This paper proposes a less conservative framework by using piecewise-quadratic generalized Lyapunov functions. Further manipulation of the problem within such framework yields a set of bilinear rather than linear matrix inequalities.

scholarly journals Delay-Dependent H∞ Control for T-S Fuzzy Systems with Local Nonlinear Models: An LMI Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhile Xia
Keyword(s):  
Linear Matrix Inequalities ◽  
Nonlinear Models ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switching Model ◽  
Delay Dependent ◽  
S Model ◽  
Takagi Sugeno ◽  
Time Systems ◽  
The Relationship

This paper studies the stabilization design scheme with H∞ performance for a large class of nonlinear discrete-time systems. The system under study is modeled by Takagi-Sugeno (T-S) model with local nonlinearity and state delay. First, the model is changed into an equivalent fuzzy switching model. And then, according to projection theorem and piecewise Lyapunov function (PLF), two new H∞ control methods are proposed for fuzzy switched systems, which consider the time delay information of the system. Finally, the relationship among all fuzzy subsystems is considered. Because the results are only expressed by a series of linear matrix inequalities (LMIs), the controller can be directly designed by the linear matrix inequalities toolbox of MATLAB.

Constrained stochastic control of positive Takagi-Sugeno fuzzy systems with Markov jumps and its application to a DC-DC boost converter

2020 ◽  
Vol 42 (16) ◽  
pp. 3234-3242
Author(s):  
Mohamed Aatabe ◽  
Fatima El Guezar ◽  
Hassane Bouzahir ◽  
Alessandro N Vargas
Keyword(s):  
Fuzzy Systems ◽  
Boost Converter ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Load Variations ◽  
Stabilization Control ◽  
Mean Square Stability ◽  
Time Formulation ◽  
Takagi Sugeno

This paper presents a stabilization control for positive, Takagi-Sugeno fuzzy systems subject to Markov jump parameters. In the continuous-time formulation, the approach guarantees mean-square stability with constraints on the control—the main condition hinges upon linear matrix inequalities. The proposed method’s usefulness is illustrated by a practical-oriented example, which was designed to control the output voltage of a DC-DC boost converter subject to both voltage and load variations driven by a Markov chain.

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