Document Zbl 0615.93004

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Englewood Cliffs, New Jersey: Prentice-Hall, Inc. XXI, 519 p.; $ 68.95 (1987).</a> </div> <div class="abstract">This book is a valuable addition to the literature on system identification and parameter estimation. Its rigorous treatment of the main topics in the system identification field should appeal to the mathematically-minded reader. The book addresses to all of those who want to get a firm grip on the basic system identification techniques that are currently available. The book contains 17 chapters and 2 appendices, which are briefly reviewed in the following. <br class="zbmathjax-paragraph">Part i: Systems and models <br class="zbmathjax-paragraph">Chapter 1 introduces, in an informal way, the basic entities of an identification exercise. Chapter 2 discusses time-invariant linear systems described by impulse responses and transfer functions, and introduces some basic notions on signal spectra and description of the disturbances. Chapter 3 discusses three main applications in which a system description is useful: simulation, prediction and control. Chapter 4 introduces a general family of transfer-function and state-space models and derives a number of results on their identifiability properties. Chapter 5 contains a brief discussion about time-varying and nonlinear models. <br class="zbmathjax-paragraph">Part ii: Methods <br class="zbmathjax-paragraph">Chapter 6 presents several nonparametric time- and frequency-domain methods, such as transient analysis, correlation analysis, Fourier and spectral analysis. Chapter 7 describes two general methods for parameter estimation: the prediction error method (PEM) and the correlation method (CM), which are shown to contain many other estimation methods as special cases. Chapter 8 establishes the consistency and identifiability properties of PEM and CM, and Chapter 9 derives the asymptotic distributions of the parameter estimates provided by these two general methods. Chapters 10 and 11 discuss various off-line and, respectively, on-line techniques to compute the PEM and CM estimates, and analyse the main problems associated with these techniques (such as convergence, numerical accuracy and fast implementation). <br class="zbmathjax-paragraph">Part iii: User’s choice <br class="zbmathjax-paragraph">Chapter 12 discusses the options and objectives that a user of system identification methods may have. Chapters 13, 14 and 15 attempt to provide some general answers to such important problems as experiment design and choice of an identification criterion. Chapter 16 discusses various techniques for model structure selection and model validation, and Chapter 17 presents two identification exercises. Finally, Appendix I contains a brief discussion of some concepts from the probability theory, and Appendix II presents the basic results on linear regressions.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A724">P.Stoica</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A3997615">Cited in <strong>2</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A3997615">Cited in <strong>764</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93-01" title="MSC2020">93-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B30" title="MSC2020">93B30</a> </td> <td class="space"> System identification </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E12" title="MSC2020">93E12</a> </td> <td class="space"> Identification in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62F12" title="MSC2020">62F12</a> </td> <td class="space"> Asymptotic properties of parametric estimators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G05" title="MSC2020">62G05</a> </td> <td class="space"> Nonparametric estimation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62J05" title="MSC2020">62J05</a> </td> <td class="space"> Linear regression; mixed models </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62Kxx" title="MSC2020">62Kxx</a> </td> <td class="space"> Design of statistical experiments </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M10" title="MSC2020">62M10</a> </td> <td class="space"> Time series, auto-correlation, regression, etc. in statistics (GARCH) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M15" title="MSC2020">62M15</a> </td> <td class="space"> Inference from stochastic processes and spectral analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M20" title="MSC2020">62M20</a> </td> <td class="space"> Inference from stochastic processes and prediction </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C05" title="MSC2020">93C05</a> </td> <td class="space"> Linear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E10" title="MSC2020">93E10</a> </td> <td class="space"> Estimation and detection in stochastic control theory </td> </tr><tr> <td class="mono"> 93E25 </td> <td class="space"> Computational methods in stochastic control (MSC2010) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asystem+identification">system identification</a>; <a href="/?q=ut%3Aparameter+estimation">parameter estimation</a>; <a href="/?q=ut%3Aimpulse+responses">impulse responses</a>; <a href="/?q=ut%3Atransfer+functions">transfer functions</a>; <a href="/?q=ut%3Asignal+spectra">signal spectra</a>; <a href="/?q=ut%3Astate-space+models">state-space models</a>; <a href="/?q=ut%3Atransient+analysis">transient analysis</a>; <a href="/?q=ut%3Acorrelation+analysis">correlation analysis</a>; <a href="/?q=ut%3AFourier+and+spectral+analysis">Fourier and spectral analysis</a>; <a href="/?q=ut%3Aprediction+error+method">prediction error method</a>; <a href="/?q=ut%3Acorrelation+method">correlation method</a>; <a href="/?q=ut%3Aexperiment+design">experiment design</a>; <a href="/?q=ut%3Amodel+structure+selection">model structure selection</a>; <a href="/?q=ut%3Amodel+validation">model validation</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0615.93004" data-ciurl="" data-biburl="/bibtex/03997615.bib" data-amsurl="/amsrefs/03997615.bib" data-xmlurl="/xml/03997615.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/03997615.pdf" title="Zbl 0615.93004 as PDF">Review PDF</a> </div> <div class="fulltexts"> </div> <div class="sfx" style="float: right;"> </div> </div> </article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; 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