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International audience; In this paper we prove that, generically, a sampled data system is strongly differentially observable provided that the number of outputs is greater than the number of inputs plus one.

This paper considers the performance output tracking for a boundary controlled Direct Contact Membrane Distillation (DCMD) system. First, the mathematical properties of a recently developed mathematical model of the DCMD system are discussed. This model consists of parabolic equations coupled at the boundary. Then, the existence and uniqueness of the solutions are analyzed, using the theory of operators. Some regularity results of the solution are also established. A particular case showing the diagonal property of the principal operator is studied. Then, based on one-side feedback law the control problem, which consists of tracking both the feed and permeate outlet temperatures of the membrane distillation system is formulated. A servomechanism and an output feedback controller are proposed to solve the control problem. In addition, an extended state observer aimed at estimating both the system state and disturbance, based on the temperature measurements of the inlet is proposed. Thus, by some regularity for the reference signal and when the disturbance vanishes, we prove the exponential decay of the output tracking error. Moreover, we show the performance of the control strategy in presence of the flux noise., 32 pages, 4 figures

International audience; This paper proposes a state observer for a coupled two dimensional partial differential equations (PDEs) system used to describe the heat transfer in a membrane distillation system for water desalination. The mathematical model based on reaction-diffusion system is introduced. Sufficient conditions for the exponential convergence of the estimation error is presented using Lyapunov method. A numerical example is also provided to illustrate the effectiveness of the proposed observer.

A previous article has investigated the problem of the preservation of the observability under sampling in the framework of compact manifolds. A natural generalization of the cited result would be to extend it to the systems globally Lipschitzian defined on non compact manifolds. A simple representative of this class of systems is constituted by the set of bilinear systems, for this particular class of systems the preservation of the property of observability has been shown in a previous work. In this paper, we deal with the preservation of the observability under sampling for globally Lipschitzian systems defined on Rn.

International audience; The aim of this paper is to study the problem of stabilization of nonlinear systems with a quadratic control. Under the assumption that a control Lyapunov function (CLF) is known, we derive necessary and sufficient conditions for the stabilization by continuous feedback controls explicitly computed. Illustrative examples are presented.