Observer Design for Robotic Systems via Takagi–Sugeno Models and Linear Matrix Inequalities

2015 ◽  
pp. 103-128
Author(s):  
Víctor Estrada-Manzo ◽  
Zsófia Lendek ◽  
Thierry-Marie Guerra
Keyword(s):  
Linear Matrix Inequalities ◽  
Observer Design ◽  
Robotic 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.

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.

POLYTOPIC OBSERVER FOR GLOBAL SYNCHRONIZATION OF SYSTEMS WITH OUTPUT MEASURABLE NONLINEARITIES

2003 ◽  
Vol 13 (03) ◽  
pp. 703-712 ◽  
Author(s):  
GILLES MILLERIOUX ◽  
JAMAL DAAFOUZ
Keyword(s):  
Dynamical Systems ◽  
Linear Matrix Inequalities ◽  
Chaos Synchronization ◽  
Observer Design ◽  
Linear Matrix ◽  
Dynamical Matrix ◽  
Matrix Inequalities ◽  
Global Synchronization ◽  
Lyapunov Approach ◽  
Special Case

Chaos synchronization has been tackled by considering the problem as a special case of an observer design. The considered dynamical systems to be synchronized have measurable nonlinearities. Their dynamical matrix is described in a polytopic way. By using the notion of polyquadratic stability, the problem of the observer synthesis is turned into the resolution of a set of Linear Matrix Inequalities (LMI) which are less conservative compared to the case of an usual quadratic Lyapunov approach. This enables to enlarge the class of systems for which synchronization can take place. The resulting matrix gain of the observer is computed by interpolating vertices gains resulting from the solution of the LMI's.

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.

Generalized dynamic observer design for quasi-LPV systems

2018 ◽  
Vol 66 (3) ◽  
pp. 225-233 ◽  
Author(s):  
A.-J. Pérez-Estrada ◽  
G.-L. Osorio-Gordillo ◽  
M. Darouach ◽  
V.-H. Olivares-Peregrino
Keyword(s):  
Linear Matrix Inequalities ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lpv Systems ◽  
Algebraic Constraints ◽  
Dynamic Observer

Abstract This paper presents a new generalized dynamic observer (GDO) for quasi-linear parameter varying (LPV) systems. It generalises the structures of the proportional observer (PO) and proportional integral observer (PIO). The design of the GDO is derived from the solution of linear matrix inequalities (LMIs) and the solution of the algebraic constraints obtained from the estimation error analysis. The efficiency of the proposed approach is illustrated by a numerical example.

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