{"day":"01","quality_controlled":"1","date_updated":"2023-10-17T08:51:18Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"abstract":[{"lang":"eng","text":"A nonlinear system possesses an invariance with respect to a set of transformations if its output dynamics remain invariant when transforming the input, and adjusting the initial condition accordingly. Most research has focused on invariances with respect to time-independent pointwise transformations like translational-invariance (u(t) -&gt; u(t) + p, p in R) or scale-invariance (u(t) -&gt; pu(t), p in R&gt;0). In this article, we introduce the concept of s0-invariances with respect to continuous input transformations exponentially growing/decaying over time. We show that s0-invariant systems not only encompass linear time-invariant (LTI) systems with transfer functions having an irreducible zero at s0 in R, but also that the input/output relationship of nonlinear s0-invariant systems possesses properties well known from their linear counterparts. Furthermore, we extend the concept of s0-invariances to second- and higher-order s0-invariances, corresponding to invariances with respect to transformations of the time-derivatives of the input, and encompassing LTI systems with zeros of multiplicity two or higher. Finally, we show that nth-order 0-invariant systems realize – under mild conditions – nth-order nonlinear differential operators: when excited by an input of a characteristic functional form, the system’s output converges to a constant value only depending on the nth (nonlinear) derivative of the input."}],"status":"public","license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"volume":"81C","isi":1,"pubrep_id":"813","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"has_accepted_license":"1","external_id":{"isi":["000403513900006"]},"file":[{"creator":"system","file_id":"4884","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_updated":"2018-12-12T10:11:29Z","file_size":1401954,"date_created":"2018-12-12T10:11:29Z","file_name":"IST-2017-813-v1+1_ZerosOfNonlinearSystems.pdf"}],"ddc":["000"],"year":"2017","article_processing_charge":"Yes (in subscription journal)","date_published":"2017-06-01T00:00:00Z","publication":"Automatica","date_created":"2018-12-11T11:49:39Z","page":"46 - 55","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"CaGu"},{"_id":"GaTk"}],"file_date_updated":"2018-12-12T10:11:29Z","language":[{"iso":"eng"}],"author":[{"first_name":"Moritz","full_name":"Lang, Moritz","id":"29E0800A-F248-11E8-B48F-1D18A9856A87","last_name":"Lang"},{"first_name":"Eduardo","full_name":"Sontag, Eduardo","last_name":"Sontag"}],"publist_id":"6391","publication_status":"published","publisher":"International Federation of Automatic Control","scopus_import":"1","oa":1,"oa_version":"Published Version","type":"journal_article","citation":{"short":"M. Lang, E. Sontag, Automatica 81C (2017) 46–55.","apa":"Lang, M., &#38; Sontag, E. (2017). Zeros of nonlinear systems with input invariances. <i>Automatica</i>. International Federation of Automatic Control. <a href=\"https://doi.org/10.1016/j.automatica.2017.03.030\">https://doi.org/10.1016/j.automatica.2017.03.030</a>","ista":"Lang M, Sontag E. 2017. Zeros of nonlinear systems with input invariances. Automatica. 81C, 46–55.","ama":"Lang M, Sontag E. Zeros of nonlinear systems with input invariances. <i>Automatica</i>. 2017;81C:46-55. doi:<a href=\"https://doi.org/10.1016/j.automatica.2017.03.030\">10.1016/j.automatica.2017.03.030</a>","chicago":"Lang, Moritz, and Eduardo Sontag. “Zeros of Nonlinear Systems with Input Invariances.” <i>Automatica</i>. International Federation of Automatic Control, 2017. <a href=\"https://doi.org/10.1016/j.automatica.2017.03.030\">https://doi.org/10.1016/j.automatica.2017.03.030</a>.","ieee":"M. Lang and E. Sontag, “Zeros of nonlinear systems with input invariances,” <i>Automatica</i>, vol. 81C. International Federation of Automatic Control, pp. 46–55, 2017.","mla":"Lang, Moritz, and Eduardo Sontag. “Zeros of Nonlinear Systems with Input Invariances.” <i>Automatica</i>, vol. 81C, International Federation of Automatic Control, 2017, pp. 46–55, doi:<a href=\"https://doi.org/10.1016/j.automatica.2017.03.030\">10.1016/j.automatica.2017.03.030</a>."},"_id":"1007","publication_identifier":{"issn":["0005-1098"]},"doi":"10.1016/j.automatica.2017.03.030","title":"Zeros of nonlinear systems with input invariances","month":"06"}