Document Zbl 1504.93290

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II: From argument principle to rightmost root assignment methods.</strong> <i>(English)</i> <a class="label nowrap" href="/1504.93290">Zbl 1504.93290</a> </h2> <div class="source"> Breda, Dimitri (ed.), Controlling delayed dynamics. Advances in theory, methods and applications. Cham: Springer. CISM Courses Lect. 604, 157-193 (2023). </div> <div class="abstract">Summary: This chapter briefly presents some “user-friendly” methods and techniques (frequency-domain approaches) for the analysis and control of linear dynamical systems in presence of delays. The presentation is as simple as possible, focusing more on the main intuitive (algebraic, geometric) ideas to develop theoretical results, and their potential use in practical applications. To fix better the ideas, scalar and second-order examples are largely discussed. Next, a particular attention will be paid to the existing links between the maximal allowable multiplicity of the characteristic roots and the spectral abscissa of the dynamical system. The underlying property – <span class="zbmathjax-textit">multiplicity induced dominancy</span> – will be particularly useful in constructing low-complexity controllers by <span class="zbmathjax-textit">partial pole placement</span>. Such an idea is particularly exploited in vibration control.<br class="zbmathjax-paragraph">For Part I, see [the first author et al., ibid. 117–155 (2023; <a href="https://doi.org/10.1007/978-3-031-01129-0_5">doi:10.1007/978-3-031-01129-0_5</a>)]<br class="zbmathjax-paragraph">For the entire collection see [<a href="/1496.93003">Zbl 1496.93003</a>].</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7626441">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7626441">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D05" title="MSC2020">93D05</a> </td> <td class="space"> Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.) in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C23" title="MSC2020">93C23</a> </td> <td class="space"> Control/observation systems governed by functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C80" title="MSC2020">93C80</a> </td> <td class="space"> Frequency-response methods in control theory </td> </tr></table> </div> <div class="software"> <h3>Software:</h3><a href="/software/42983">p3delta</a>; <a href="/software/4968">DLMF</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 1504.93290" data-ciurl="/ci/07626441" data-biburl="/bibtex/07626441.bib" data-amsurl="/amsrefs/07626441.bib" data-xmlurl="/xml/07626441.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07626441.pdf" title="Zbl 1504.93290 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/10.1007/978-3-031-01129-0_6" aria-label="DOI for “Counting characteristic roots of linear delay differential equations. II: From argument principle to rightmost root assignment methods”" title="10.1007/978-3-031-01129-0_6">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://hal.science/hal-03634874" title="Open Access at HAL">HAL </a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ahlfors, L. V. (1979). Complex analysis. McGraw-Hill, Inc. · <a href="/0395.30001" class="nowrap">Zbl 0395.30001</a></td> </tr><tr> <td>[2]</td> <td class="space">Balogh, T., Boussaada, I., Insperger, T., & Niculescu, S. -I. (2022). Conditions for stabilizability of time-delay systems with real-rooted plant. 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