Document Zbl 1264.34006

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Math.</a> <a href="/?q=in%3A318621" title="Articles in this Issue">2012, Article ID 725783, 46 p. (2012)</a>. </div> <div class="abstract">Summary: We review some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The framework prsented in this paper makes it possible to provide simpler formulation and strengthen, generalize, or provide alternative interpretation of the existing results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6172978">Cited in <strong>21</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34-02" title="MSC2020">34-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K40" title="MSC2020">34K40</a> </td> <td class="space"> Neutral functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K20" title="MSC2020">34K20</a> </td> <td class="space"> Stability theory of functional-differential equations </td> </tr></table> </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 1264.34006" data-ciurl="/ci/06172978" data-biburl="/bibtex/06172978.bib" data-amsurl="/amsrefs/06172978.bib" data-xmlurl="/xml/06172978.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06172978.pdf" title="Zbl 1264.34006 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.5402/2012/725783" aria-label="DOI for “A review of some subtleties of practical relevance for time-delay systems of neutral type”" title="10.5402/2012/725783">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Brayton, R., Small signal stability criterion for electrical networks containing lossless transmission lines, IBM Journal of Research and Development, 12, 6, 431-440 (1968) · <a href="/0172.20703" class="nowrap">Zbl 0172.20703</a> · <a href="https://doi.org/10.1147/rd.126.0431" class="nowrap">doi:10.1147/rd.126.0431</a></td> </tr><tr> <td>[2]</td> <td class="space">Manitius, A. 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