Examination of the SPR condition in output error parameter estimation
It has been discussed in this paper that a sharp stability-instability boundary exists and limits the spectral content of the regressor vector \(\phi\) when the strictly positive real (SPR) condition is not satisfied. A condition is given which delimits the sharp stability-instability boundary in the case of slow estimation, whereas local stability properties are guaranteed by a more conservative signal-dependent average SPR condition. For a transfer function H(z), the stability is assured if \(\phi\) is such that ``on average H'' behaves as an SPR transfer function. This paper extends the continuous-time results of \textit{P. Kokotovic, B. Riedle} and \textit{L. Praly} [Syst. Control Lett. 6, 7-14 (1985; Zbl 0569.93050)], and the discrete-time algorithm to be analyzed is an A-class identifier of \textit{I. D. Landau} [Adaptive control: The model reference approach (New York 1979)]; \textit{G. C. Goodwin} and \textit{K. S. Sin} [Adaptive filtering, prediction and control (Englewood Cliffs 1984)]. For some test inputs the output of a non-matchable plant can still be matched by the output of a lower order model. One theorem and two corollaries are given. An example in which the output error algorithm is used to estimate the parameters is also included.
scientific article; zbMATH DE number 4018914
scientific article