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The identification of the quadratic in-the-state systems (QSS) is the objective of this paper. This class, on its own, enjoys a useful model for many nonlinear dynamic systems. Moreover, it represents a bilinear system in a feedback loop. In order to identify QSS, we propose to minimize the output error with respect to the system's parameters using a local gradient search. In order to reduce the amount of gradient search to the minimal value, we propose an efficient implementation of the algorithm by projecting out the directions that do not change the output error function. Furthermore, we extend the proposed method to deal with multiple short experiments.