Elimination of real positivity condition and error filtering in parallel MRAS

For a particular degree of persistent excitation, the commonly accepted strict positive realness (SPR) condition and associated error filtering in the design of model reference adaptive system (MRAS) are removed. It is shown that the parameter estimation vector remains bounded and the output error converges asymptotically to zero for a stable reference model. The proof proceeds with simple algebra, and does not rely on the commonly used hyperstability theorem and positivity concept.