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On the need of projections in input‐error model reference adaptive control

The main objective of this note is to contribute, if modestly, toward the understanding of the input‐error model reference adaptive control scheme revealing an instability mechanism that arises if the projection of the plant high‐frequency gain coefficient estimate is omitted. In addition, a self‐contained proof of global convergence of the scheme with the projections for a simple first‐order plant is given.