A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Copyright [2004] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Recent years have seen a great deal of interest in implicit nonlinear systems, which are used in many different engineering applications. This study is dedicated to presenting a new method of fuzzy unknown inputs observer design to estimate simultaneously both non-measurable states and unknown inputs of continuous-time nonlinear implicit systems defined by Takagi-Sugeno (T-S) models with unmeasurable premise variables. The suggested observer is based on the singular value decomposition approach and rewritten the continuous-time T-S implicit models into an augmented fuzzy system, which gathers the unknown inputs and the state vector. The exponential convergence condition of the observer is established by using the Lyapunov theory and linear matrix inequalities are solved to determine the gains of the observer. Finally, the effectiveness of the suggested method is then assessed using a numerical application. It demonstrates that the estimated variables and the unknown input converge to the real variables accurately and quickly (less than 0.5 s)

Approches non-quadratiques pour la commande robuste des descripteurs flous de type T-S

International audienceDans ce papier, nous proposons une synthèse de contrôleurs pour la stabilisation robuste des systèmes descripteurs de type Takagi-Sugeno (T-S) incertains et perturbés. Celle-ci est basée sur l'utilisation d'une fonction de Lyapunov Non-Quadratique dite Fonction de Lyapunov Floue (FLF) ainsi que sur une loi de commande dite non-PDC (Non-Parallel-Distributed-Compensation). Les problèmes de stabilité et de synthèse de contrôleur H ∞ sont alors formulés en termes d'Inégalités Matricielles Linéaires (LMI). Enfin un exemple académique est proposé. Mots clés-Commande non linéaire, Commande floue, Takagi-Sugeno, Commande robuste, Descripteurs, Fonction de Lyapunov non-quadratique, LMI

Nouvelles conditions LMI de stabilisation non quadratique pour descripteurs flous de type T-S

International audienceThis paper presents new stability conditions for Takagi-Sugeno (T-S) descriptor systems based on descriptors redundancy. These conditions are obtained via fuzzy Lyapunov function (FLF) and a non-Parallel-Distributed-Compensation (non-PDC) control law. First, LMI stability conditions for the considered class of systems without external disturbances are proposed. Then, the problem of ∞ Η based controller design is treated. Finally, a numerical example is proposed to illustrate the efficiency of the proposed approaches.Ce papier présente de nouvelles conditions de stabilité pour les systèmes descripteurs de type Takagi-Sugeno (T-S) basés sur la redondance des descripteurs. Ces conditions sont obtenues via une fonction floue de Lyapunov (FLF) et une loi de commande non-Parallel-Distributed-Compensation (non-PDC). Tout d'abord, les conditions de stabilité LMI pour la classe des systèmes considérée sans perturbations externes sont proposées. Ensuite, le problème de synthèse d'un contrôleur ∞ Η est traité. Enfin, un exemple numérique illustre l'efficacité des approches proposées

Conditions de stabilité LMI pour la classe des systèmes descripteurs flous incertains de type T-S

International audienceDans cette étude, des conditions de stabilité pour la classe des descripteurs flous incertains de type Takagi-Sugeno (T-S) sont proposées. Celles-ci sont basées sur une fonction candidate de Lyapunov quadratique. Afin de permettre leur résolution par les outils classiques de l'optimisation convexe, les conditions proposées sont données sous forme d'inégalités matricielles linéaires (LMI). Enfin, un exemple académique illustre l'efficacité de l'approche proposée

Convergence d'observateurs flous sous formes descripteurs : application à l'homme en station debout

International audienceUne classe d'observateurs non linéaires sous forme descripteurs basée sur une modélisation de type Takagi-Sugeno (TS) est décrite. Les conditions de convergence de l'erreur de reconstruction sont obtenues sous la forme de problèmes LMI. L'intérêt de ce type de représentation est, pour certains modèles non linéaires, de réduire la conservativité des résultats classiques. Cette réduction se fait au travers de la réduction du nombre de règles du modèle TS. Une application à la biomécanique de l'homme en station debout est proposée. Un observateur à entrées inconnues est défini afin d'estimer les vitesses et couples articulaires à partir de mesures de positions obtenues par un système optoélectronique de capture du mouvement

Observer Design for a Class of Nonlinear Descriptor Systems: A Takagi-Sugeno Approach with Unmeasurable Premise Variables

The Takagi-Sugeno (T-S) fuzzy observer for dynamical systems described by ordinary differential equations is widely discussed in the literature. The aim of this paper is to extend this observer design to a class of T-S descriptor systems with unmeasurable premise variables. In practice, the computation of solutions of differential-algebraic equations requires the combination of an ordinary differential equations (ODE) routine together with an optimization algorithm. Therefore, a natural way permitting to estimate the state of such a system is to design a procedure based on a similar numerical algorithm. Beside some numerical difficulties, the drawback of such a method lies in the fact that it is not easy to establish a rigorous proof of the convergence of the observer. The main result of this paper consists in showing that the state estimation problem for a class of T-S descriptor systems can be achieved by using a fuzzy observer having only an ODE structure. The convergence of the state estimation error is studied using the Lyapunov theory and the stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an application to a model of a heat exchanger pilot process is given to illustrate the performance of the proposed observer

Delay-Dependent Finite-Time H

Delay-dependent finite-time H∞ controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time H∞ controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the H∞ performance to a prescribed disturbance attenuation level γ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI). Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a H∞ performance level