Examination of the SPR condition in output error parameter estimation
type: Item
instance of: scholarly article
title: Examination of the SPR condition in output error parameter estimation
zbMATH Open document ID: 0626.93068
DOI: 10.1016/0005-1098(86)90055-5
author: B. Riedle
author: Laurent Praly
author: P. V. Kokotović
published in: Automatica
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 93E25
zbMATH DE Number: 4018914
zbMATH Keywords: stability-instability boundary
zbMATH Keywords: strictly positive real (SPR) condition
zbMATH Keywords: slow estimation
MaRDI profile type: Publication
full work available at URL: 0005-1098(86)90055-5
OpenAlex ID: W2014342391
cites work: Q3799870
cites work: An asymptotic error analysis of identifiers and adaptive observers in the presence of parasitics
cites work: On a stability criterion for continuous slow adaptation
cites work: Q3931079
cites work: On positive real transfer functions and the convergence of some recursive schemes
cites work: Stability of slow adaptation for non-SPR systems with disturbances
cites work: A stability-instability boundary for disturbance-free slow adaptation with unmodeled dynamics
description: scientific article; zbMATH DE number 4018914