ScienceDirect IFAC-PapersOnLine 48-26 (2015) 213–217 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2015.11.139 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Almost sure exponential stability, stochastic differential equation, bang-bang control, observer-based control. 1. INTRODUCTION Many authors was interested during the last years by renewable energies such as wind energy (Boukhezzar and Siguerdidjane, 2005; Wang and Weiss, 2006; Bianchi et al., 2005; Lescher et al., 2006). This is due to the need to have new renawable and clean energy sources. This paper is a preliminary work concerning the control analy- sis and design for some renewable energy production systems. in fact, these systems get a great importance these last decades. Our interest is firstly focused on the study of wind turbines because they are one of the most promising energy sources. Wind turbines whose functioning is based on a Doubly Fed Induction Generator (DFIG which form the object of our study) are widely recognized in the industry as one of the most promising wind turbines configuration, particularly for the large productivity of the offshore wind farms. Generally the wind turbines control is made without taking into account the wind and turbine dynamical aspects. This causes a large efficiency losses (Boukhezzar and Siguerdidjane, 2005; Wang and Weiss, 2006; Bianchi et al., 2005). The considered H ∞ LPV (Linear Parameter Varying) control takes into account these important dynamics to improve the performances and to ensure better energy production while minimizing the effect of disturbances on the controlled outputs. For this purpose, we first present a DFIG modelisation procedure to obtain an LPV model. Then the theoretical part of our work deals with the H ∞ state feedback control for linear parameter varying systems; this parameter involved in affine manner the system equation. Many authors have treated the problem of LPV systems control using a gain scheduling approach or a parameter-dependent Lyapunov functions (see (Becker and Packard, 1994; Packard, 1994) and (Bara et al., 2001)). Our proposed approach avoids the use of multi-convexity even when the state matrix of the system is affine (Gahinet and Apkarian, 1994; Gahinet et al., 1996; Yu et al., 2002). The multi-convexity is one of the approach used to solve control problems whose resolution leads to multiply some affine terms between them, when we want to solve them using LMI (Linear Matrix Inequality) approach. Our method avoids this by introducing additional degrees of freedom in solving the problem. Therefore the chosen Lyapunov matrix is no longer multiplied by the closed loop dynamic one using a descriptor approach (Chughtai and Munro, 2004). This Lyapunov matrix is chosen with an affine structure similar to the system dynamic matrix. Thus, an additional degree of freedom is introduced to solve the problem, since the Lyapunov matrix is no longer considered constant contrary to many other references (see (Souley Ali et al., 2006) and references therein). In addition, taking into account the particular system structure LPV, considered in this paper, the designed controller is dif- ferent from that proposed in (Souley Ali et al., 2006). Indeed, here we propose an LPV controller structure which is similar to the system one. In (Souley Ali et al., 2006), the controller gain was constant contrary to the proposed approach, which permit a gain in terms of degrees of freedom and performances. Finally, the proposed method is then applied to a wind turbine model to show its effectiveness. 2. PRELIMINARIES Let us consider a nonlinear system given in the following form: ˙ X = f (X , U, w) (1) Z = g(X , U, w) (2) Abstract: This paper is devoted to the synthesis of an H ∞ LPV state feedback controller, applied to a wind turbine which is described by an LPV model. Firstly, we focus on the modeling of wind turbines, to propose a model that describes as good as possible the system behaviour. A new approach that allows us, via LMIs, to design an LPV controller for a class of LPV systems is then presented. The interest of the approach is to decouple the system dynamic matrix and the lyapunov one using a desriptor approach. Finally, to illustrate the proposed control strategy, some simulation results are presented. * CRAN UMR 7039 CNRS, Universit´ e de Lorraine, 186 rue de Lorraine, 54400 Cosnes et Romain, France.(harouna.souley@univ-lorraine.fr, mohamed.darouach@univ-lorraine.fr, michel.zasadzinski@univ-lorraine.fr, marouane.alma@univ-lorraine.fr). Harouna Souley Ali * Mohamed Darouach * Michel Zasadzinski * Marouane Alma * An H ∞ LPV control for a class of LPV systems using a descriptor approach: Application to a wind turbine mode