The goal of the present work is to achieve nonlinear semi-global output feedback stabilization of variable speed grid connected direct drive wind turbine generator DDWTG systems under wind energy conversion systems to provide the electricity demand for electrical networks. The study will address the sensorless control of variable speed wind energy generation systems, namely optimized rotor speed and direct-axis current control to determine the most appropriate structure and to improve both robustness and reliability of this kind of distributed generators. The proposed nonlinear observer is robust with respect to measurements error and perturbations of the sampling schedule. The simulation results of the case study support the presented main theorem that reflects the effect of measurement errors and the improvement with respect to global convergence properties. The novelty of the present study resides in taking into account the difficulties and control problem complexity that faced the nonlinear output feedback control undergo: Preliminaries and Notations Throughout this paper, |.| means the absolute value. Let us consider R def = (−∞, ∞), R + def = (0, ∞) positive real number space, R + 0 = [0, ∞], and let us define ||.|| be the Euclidean norm or the induced matrix norm. For p, q, n, m ∈ N , set of natural numbers, R p×q represents the set of real matrices of order p × q and I p ∈ I R p× p stands for the identity matrix of order p × p. The notation ||P||, for P ∈ R p×q , represents the L 2-norm of P and X T , represent the transposed vector of X. One say that α I n ≤ P ≤ β I n where P ∈ R n×n if, λmin (P) ≥ α and λmax (P) ≥ β where λmin (.) and λmax (.) denote, respectively the smallest and the biggest eigenvalues of the square matrix. In all this study, the initial boundary time is called t 0 ∈ [0, ∞).
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