Document Zbl 1402.34078

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Vietnam.</a> <a href="/?q=in%3A419060" title="Articles in this Issue">43, No. 4, 715-735 (2018)</a>. </div> <div class="abstract">Summary: The solvability and stability analyses of linear time invariant systems of delay differential-algebraic equations (DDAEs) are analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in terms of spectral conditions. Furthermore, examples are delivered to demonstrate that the eigenvalue-based approach in analyzing the exponential stability of dynamical systems is only valid for a special class of DDAEs, namely, <span class="zbmathjax-textit">non-advanced</span>. Then, a new concept of weak stability is proposed and studied for DDAEs whose matrix coefficients pairwise commute.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6970050">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K32" title="MSC2020">34K32</a> </td> <td class="space"> Implicit functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L05" title="MSC2020">65L05</a> </td> <td class="space"> Numerical methods for initial value problems involving ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65H10" title="MSC2020">65H10</a> </td> <td class="space"> Numerical computation of solutions to systems of 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><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K06" title="MSC2020">34K06</a> </td> <td class="space"> Linear functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K08" title="MSC2020">34K08</a> </td> <td class="space"> Spectral theory of functional-differential operators </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adifferential-algebraic+equations">differential-algebraic equations</a>; <a href="/?q=ut%3Atime+delay">time delay</a>; <a href="/?q=ut%3Amatrix+polynomials">matrix polynomials</a>; <a href="/?q=ut%3Acommutative">commutative</a>; <a href="/?q=ut%3Aexponential+stability">exponential stability</a>; <a href="/?q=ut%3Aweak+stability">weak stability</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 1402.34078" data-ciurl="/ci/06970050" data-biburl="/bibtex/06970050.bib" data-amsurl="/amsrefs/06970050.bib" data-xmlurl="/xml/06970050.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06970050.pdf" title="Zbl 1402.34078 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/s40306-018-0279-7" aria-label="DOI for “Spectral characterizations of solvability and stability for delay differential-algebraic equations”" title="10.1007/s40306-018-0279-7">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1802.01148"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ascher, UM; Petzold, LR, The numerical solution of delay-differential algebraic equations of retarded and neutral type, SIAM J. 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