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Adaptive control via output-feedback is considered for SISO, feedback linearizable, minimum-phase, discrete-time nonlinear systems. The class of systems consists of linear systems followed by a nonlinear element with further nonlinearities depending on the (delayed) outputs. The coefficients of the transfer function of the linear part are assumed unknown, and either the nonlinear element acting on the output or the nonlinearities acting on the (delayed) outputs are not limited to sector-type conditions.
Song et al. (Tue,) studied this question.