[{"abstract":[{"lang":"eng"}],"type":"journal_article","pubrep_id":"813","oa_version":"Published Version","file":[{"file_name":"IST-2017-813-v1+1_ZerosOfNonlinearSystems.pdf","access_level":"open_access","content_type":"application/pdf","file_size":1401954,"creator":"system","relation":"main_file","file_id":"4884","date_updated":"2018-12-12T10:11:29Z","date_created":"2018-12-12T10:11:29Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1007","ddc":[],"status":"public","article_processing_charge":"Yes (in subscription journal)","uri_base":"https://research-explorer.ista.ac.at","has_accepted_license":"1","day":"01","dc":{"identifier":["https://research-explorer.ista.ac.at/record/1007","https://research-explorer.ista.ac.at/download/1007/4884"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"description":["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) -> u(t) + p, p in R) or scale-invariance (u(t) -> pu(t), p in R>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."],"creator":["Lang, Moritz","Sontag, Eduardo"],"source":["Lang M, Sontag E. Zeros of nonlinear systems with input invariances. Automatica. 2017;81C:46-55. doi:10.1016/j.automatica.2017.03.030"],"rights":["https://creativecommons.org/licenses/by/4.0/","info:eu-repo/semantics/openAccess"],"publisher":["International Federation of Automatic Control"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1016/j.automatica.2017.03.030","info:eu-repo/semantics/altIdentifier/issn/0005-1098","info:eu-repo/semantics/altIdentifier/wos/000403513900006","info:eu-repo/grantAgreement/EC/FP7/291734"],"subject":["ddc:000"],"title":["Zeros of nonlinear systems with input invariances"],"date":["2017"],"language":["eng"]},"scopus_import":"1","date_published":"2017-06-01T00:00:00Z","citation":{"ista":"Lang M, Sontag E. 2017. Zeros of nonlinear systems with input invariances. Automatica. 81C, 46–55.","ieee":"M. Lang and E. Sontag, “Zeros of nonlinear systems with input invariances,” Automatica, vol. 81C. International Federation of Automatic Control, pp. 46–55, 2017.","apa":"Lang, M., & Sontag, E. (2017). Zeros of nonlinear systems with input invariances. Automatica. International Federation of Automatic Control. https://doi.org/10.1016/j.automatica.2017.03.030","mla":"Lang, Moritz, and Eduardo Sontag. “Zeros of Nonlinear Systems with Input Invariances.” Automatica, vol. 81C, International Federation of Automatic Control, 2017, pp. 46–55, doi:10.1016/j.automatica.2017.03.030.","short":"M. Lang, E. Sontag, Automatica 81C (2017) 46–55.","chicago":"Lang, Moritz, and Eduardo Sontag. “Zeros of Nonlinear Systems with Input Invariances.” Automatica. International Federation of Automatic Control, 2017. https://doi.org/10.1016/j.automatica.2017.03.030."},"publication":"Automatica","page":"46 - 55","ec_funded":1,"publist_id":"6391","file_date_updated":"2018-12-12T10:11:29Z","creator":{"login":"apreinsp","id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"},"author":[{"id":"29E0800A-F248-11E8-B48F-1D18A9856A87","first_name":"Moritz","last_name":"Lang"},{"last_name":"Sontag","first_name":"Eduardo"}],"volume":"81C","dini_type":"doc-type:article","date_created":"2018-12-11T11:49:39Z","date_updated":"2023-10-17T08:51:18Z","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"CaGu"},{"_id":"GaTk","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"publication_status":"published","publication_identifier":{"issn":[]},"month":"06","language":[{}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":[]},"oa":1,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1"}]