Document Zbl 07889224

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Control</a> <a href="/?q=in%3A515520" title="Articles in this Issue">25, No. 4, 3242-3252 (2023)</a>. </div> <div class="abstract">Summary: This paper presents a bicoprime factorization (BCF) approach to deal with various stability problems for linear discrete time-varying (LTV) systems within the framework of nest algebra. Based on the bicoprime factorization, we give necessary and sufficient conditions for (strongly) simultaneous stabilization of three systems, which generalize similar results for systems by coprime factorization (CF). Finally, when the bicoprime factorization for the plant and controller has additive perturbations, we derive sufficient conditions using the norm inequality for robust stability of the system.<br class="zbmathjax-paragraph">© 2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D15" title="MSC2020">93D15</a> </td> <td class="space"> Stabilization of systems by feedback </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Abicoprime+factorization">bicoprime factorization</a>; <a href="/?q=ut%3Anest+algebra">nest algebra</a>; <a href="/?q=ut%3Arobust+stability">robust stability</a>; <a href="/?q=ut%3Asimultaneous+stabilization">simultaneous stabilization</a>; <a href="/?q=ut%3Atransitivity">transitivity</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 07889224" data-ciurl="/ci/07889224" data-biburl="/bibtex/07889224.bib" data-amsurl="/amsrefs/07889224.bib" data-xmlurl="/xml/07889224.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07889224.pdf" title="Zbl 07889224 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/10.1002/asjc.3028" aria-label="DOI for “Stability analysis for linear time-varying systems using bicoprime factorization”" title="10.1002/asjc.3028">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">Vidyasagar, M., Control system synthesis: A factorization approach, 1985, Mandgan Claypool Publisher: Cambridge, MA · <a href="/0655.93001" class="nowrap">Zbl 0655.93001</a> · <a href="https://doi.org/10.1016/0005‐1098(86)90058‐0" class="nowrap">doi:10.1016/0005‐1098(86)90058‐0</a></td> </tr><tr> <td>[2]</td> <td class="space">Smith, M. 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