Robust Hinf tracking control design for a class of switched linear systems using descriptor redundancy approach

International audienceThe work presented in this paper concerns the output feedback tracking control for a class of Switched Linear Systems (SLS) with external disturbances. The main result is based on a descriptor redundancy formulation of the closedloop dynamics. The proposed approach allows the avoiding of the crossing terms appearance between the controller's and the switched system's matrices leading to easier Linear Matrix Inequality (LMI) formulation. Multiple Lyapunov functional methods are utilized to the stability analysis and controller design. By introducing the Proportional-Derivative (PD) controller, a robust Hinf output feedback tracking performance has been satisfied. The efficiency of the proposed synthesis procedure has been illustrated by a numerical example

Design of a decentralized tracking control for a class of switched large-scale systems

International audienceThis paper proposes a new design of a decentralized output-feedback tracking control for a class of switched large-scale systems with external bounded disturbances. The controller proposed herein is synthesized to satisfy the robust H tracking performance with local disturbance attenuation levels. Based on multiple switched Lyapunov functions, sufficient conditions proving the existence of the proposed controller are formulated in terms of Linear Matrix Inequalities (LMI). A deep simulation is proposed to illustrate the effectiveness of the obtained results

Observer Design for Takagi-Sugeno Descriptor System with Lipschitz Constraints

This paper investigates the design problem of observers for nonlinear descriptor systems described by Takagi-Sugeno (TS) system; Depending on the available knowledge on the premise variables two cases are considered. First a TS descriptor system with measurables premises variables are proposed. Second, an observer design which satisfying the Lipschitz condition is proposed when the premises variables are unmeasurables. 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). Examples are included to illustrate those methods.Comment: 13 pages,5 figures; International Journal of Instrumentation and Control Systems (IJICS) Vol.2, No.2, April 201

Stabilisation robuste des systèmes Takagi-Sugeno par lois de commande à commutations

International audienceDans cet article, la stabilisation des systèmes non linéaires incertains et perturbés est abordée à travers une modélisation sous forme de modèles flous de type Takagi-Sugeno (T-S) à commutations. Afin d'assurer la stabilisation robuste des systèmes T-S incertains et perturbés à commutations garantissant la minimisation de l'effet des perturbations externes, une méthodologie de synthèse quadratique H∞ de lois de commande floues à commutations est proposée. Les conditions de stabilité sont exprimées en termes d'Inégalités Linéaires Matricielles (LMI). Finalement, un exemple numérique illustre l'efficacité de l'approche proposée

Contribution on the control law synthesis's of Takagi-Sugeno and/or hybrid interconnected systems

Les travaux de cette thèse portent sur la stabilisation des systèmes non linéaires à grandes dimensions. Il s’agit de décomposer le système de grandes dimensions en un ensemble de n sous-systèmes interconnectés. Ensuite, en tenant compte de la nature des sous-systèmes, un ensemble de lois de commande décentralisées, composée de n lois de commande locale, peut être synthétisé. Ainsi, chaque loi de commande locale est associée à un sous-système et permet de le stabiliser indépendamment des autres sous-systèmes. Trois classes de systèmes sont ainsi traitées dans le cadre de cette thèse : les systèmes non linéaires interconnectés et les systèmes hybrides interconnectés (linéaires ou non linéaires).Premièrement, on s’est intéressé à l’étude de la stabilisation des systèmes non linéaires interconnectés représentées par des multi-modèles de type Takagi-Sugeno (TS). En effet, un multi-modèle TS permet de représenter un système non linéaire affine par un ensemble de modèles linéaires interconnectés par des fonctions non linéaires. Afin de réduire le conservatisme des approches quadratiques de Lyapunov existantes, de nouvelles conditions écrites sous forme d’inégalités linéaires matricielles (LMI) ont été proposées sur la base d’une fonction non quadratique de Lyapunov candidate. Ces conditions permettent ainsi la synthèse des contrôleurs TS décentralisés proposés. Dans le but d’étendre les résultats obtenus au cas des systèmes non linéaires et hybrides de grandes dimensions, on s’est ensuite intéressé à l’étude de la stabilisation des systèmes linéaires à commutations interconnectés via l’emploi de fonctions multiples de Lyapunov. Enfin, des conditions de stabilisation pour les systèmes non linéaires interconnectés à commutations, composés de sous-systèmes TS à commutations, ont été proposées sous forme LMI.This thesis focuses on the stabilization of nonlinear large scale systems. Hence, a global large scale systemcan be described by a set of n interconnected subsystems. Then, based on the subsystem’s nature, adecentralized control law, composed of a set of n local control law is proposed. Each local control law isable to stabilize the subsystem for which it is synthesized. In this thesis, three classes of dynamical systemsare considered : nonlinear interconnected systems, switched linear interconnected systems and switchednonlinear interconnected systems.First, based on Takagi Sugeno (TS) modeling, the decentralized stabilization of nonlinear interconnectedsystems has been studied. In order to relax quadratic Lyapunov approaches, one has considered nonquadratic Lyapunov functions. Then, based on multiple Lyapunov switched functions, the stabilization oflarge scale linear switched systems is proposed. Hence, a decentralized switched control law designmethodology has been developed to ensure the stability of the proposed class of hybrid systems. Finally,the stabilization of nonlinear switched interconnected systems as been considered such that each nonlinearsubsystem is described by a TS model

Design of a decentralized tracking control for a class of switched large-scale systems

International audienceThis paper proposes a new design of a decentralized output-feedback tracking control for a class of switched large-scale systems with external bounded disturbances. The controller proposed herein is synthesized to satisfy the robust H tracking performance with local disturbance attenuation levels. Based on multiple switched Lyapunov functions, sufficient conditions proving the existence of the proposed controller are formulated in terms of Linear Matrix Inequalities (LMI). A deep simulation is proposed to illustrate the effectiveness of the obtained results

Decentralized stabilization of interconnected switched descriptors via a multiple switched Lyapunov functional

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Design of a decentralized tracking control for a class of switched large-scale systems

International audienceThis paper proposes a new design of a decentralized output-feedback tracking control for a class of switched large-scale systems with external bounded disturbances. The controller proposed herein is synthesized to satisfy the robust H tracking performance with local disturbance attenuation levels. Based on multiple switched Lyapunov functions, sufficient conditions proving the existence of the proposed controller are formulated in terms of Linear Matrix Inequalities (LMI). A deep simulation is proposed to illustrate the effectiveness of the obtained results