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In this paper, the problem of adaptive observer design for the class of state affine systems is discussed. The discussion is based on recent results on adaptive observer with exponential rate of convergence obtained for multi-input–multi-output linear time varying systems on the one hand, and the well-known Kalman-like design for state affine systems on the other. In particular the relationship between both designs is emphasized, showing how they can even be equivalent. The interest of such an adaptive observer for state affine systems is illustrated by the example of state and parameter estimation for the Lorenz chaotic system. The observer performances are illustrated via simulation.