On the stability of parallel MRAS with an AEF

The stability of the parallel model reference adaptive system (MRAS) with an adjustable error filter (AEF) is discussed. It is shown that the null solutions of the parameter error vector and output error are asymptotically stable if the parameter update recursion employs time-varying adaptation gain matrix. The analysis proceeds with simple algebra, eliminates the strict positive realness (SPR) machinery, and does not resort to Lyapunov's direct method and hyperstability.