AbstractAdaptive control schemes based on the recursive least squares (RLS) estimation technique are analysed in this paper. First, under the assumption that the asymptotically estimated system does not present pole‐zero cancellations, a general stability result is proven. Such a result does not require the system to be minimum phase. Then it is shown that on the grounds of the stability property the control system attains asymptotic optimality.The results of the present paper rely on previous work by Rootzen and Sternby concerning the consistency of RLS estimates and are intended as a first step in the extension of Kumar's work in adaptive control to non‐minimum phase syst
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