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.

Stable and Optimal Controller Design for Takagi-Sugeno Fuzzy Model Based Control Systems via Linear Matrix Inequalities

2016 ◽  
Vol 14 (3) ◽  
pp. 31-40 ◽  
Author(s):  
M. Namazov ◽  
A. Alili
Keyword(s):  
Nonlinear System ◽  
Control Systems ◽  
Linear Matrix Inequalities ◽  
Linear Models ◽  
Fuzzy Model ◽  
Design Procedure ◽  
Optimal Performance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Takagi Sugeno

AbstractThis paper deals with a systematic design procedure that guarantees the stability and optimal performance of the nonlinear systems described by Takagi-Sugeno fuzzy models. Takagi-Sugeno fuzzy model allows us to represent a nonlinear system by linear models in different state space regions. The overall fuzzy model is obtained by fuzzy blending of these linear models. Then based on this model, linear controllers are designed for each linear model using parallel distributed compensation. Stability and optimal performance conditions for Takagi-Sugeno fuzzy control systems can be represented by a set of linear matrix inequalities which can be solved using software packages such as MATLAB’s LMI Toolbox. This design procedure is illustrated for a nonlinear system which is described by a two-rule Takagi-Sugeno fuzzy model. The fuzzy model was built in MATLAB Simulink and a code was written in LMI Toolbox to determine the controller gains subject to the proposed design approach.

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.

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.

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.

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