Modified output error identification-elimination of the SPR condition

In this note, we present a modified adaptive output error algorithm for identification. We refer to both the continuous time and the discrete time cases. In the standard algorithm, stability requires that a certain transfer function should be strictly positive real (SPR); however, in the present algorithm, the SPR condition, which is difficult to satisfy, is eliminated. This is achieved by adding a fixed feedback gain. When there exists an a priori partial knowledge about the parameters of the plant, we provide a simple procedure to design that gain. An illustrative example comparing the modified algorithm to the standard one is provided