{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:59:09Z","timestamp":1787324349485,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>We examine to what extent nonlinear input-disturbance systems that are connected by a simulation relation share certain controllability properties. We derive several results that fit within the paradigm that if there is a simulation relation of a system $A$ by a system $B$, and if system $A$ has a specified controllability property, then system $B$ has that same property. As expected, one can only turn the paradigm into actual theorems by imposing appropriate assumptions on the systems and\/or the simulation relation. We prove three such results. The first result we obtain deals with the property of complete controllability, where we impose minimal assumptions on the input-disturbance systems but require that the simulation relation be the graph of a smooth surjection between the systems' state spaces that satisfies a certain compactness condition. The second result deals with a somewhat weaker notion of controllability modulo the kernel of a linear mapping, where it is assumed that system $B$ is \u201calmost linear,\u201d but where the simulation relation is the zero set of a smooth mapping of a specific form (but is not necessarily the graph of a function). The third result (and the most difficult to prove) also deals with the property of complete controllability and, while imposing minimal assumptions on the input-disturbance systems, allows the simulation relation to be the zero set of a smooth function (and so not necessarily a graph), though other somewhat restrictive assumptions do have to be imposed. We conclude with several examples to illustrate our results.<\/jats:p>","DOI":"10.1137\/130949646","type":"journal-article","created":{"date-parts":[[2015,6,2]],"date-time":"2015-06-02T12:27:53Z","timestamp":1433248073000},"page":"1346-1374","source":"Crossref","is-referenced-by-count":9,"title":["Simulation Relations and Controllability Properties of Linear and Nonlinear Control Systems"],"prefix":"10.1137","volume":"53","author":[{"given":"Kevin A.","family":"Grasse","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nancy","family":"Ho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,6,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90010-8"},{"key":"atypb2","first-page":"302","author":"C\u030cerans K.","year":"1993","journal-title":"Berlin"},{"key":"atypb3","first-page":"676","author":"P. 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Isidori,\n                      Nonlinear Control Systems\n                      , 3rd ed., Springer-Verlag, New York, 1995.","DOI":"10.1007\/978-1-84628-615-5"},{"key":"atypb14","unstructured":"R. Milner,\n                      A Calculus of Communicating Systems\n                      , Laboratory for Foundations of Computer Science, University of Edinburgh, Edinburgh, 1986."},{"key":"atypb15","unstructured":"R. Milner,\n                      Communication and Concurrency\n                      , Prentice-Hall, Upper Saddle River, NJ, 1989."},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"H. Nijmeijer and A. 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Warner,\n                      Foundations of Differentiable Manifolds and Lie Groups\n                      , Scott, Foresman and Co., Glenview, IL, 1971."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130949646","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:22:19Z","timestamp":1787322139000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130949646"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130949646"],"URL":"https:\/\/doi.org\/10.1137\/130949646","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}