A class of implicit model reference adaptive controllers is described designed via feedback Kalman-Yakubovich lemma. Stability conditions of adaptive system are formulated. An example of application to the adaptive stabilization of distillation column is given. A new simple solution of adaptive stabilization problem for minimum phase plants with arbitrary relative degree is also suggested based on implicit reference model and a parallel feedforward compensator (filter) of order k-1 making plant hyper minimum phase.