{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:12Z","timestamp":1760240232825,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Russian Scientific Foundation","award":["16-19-00046-P"],"award-info":[{"award-number":["16-19-00046-P"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper considers the disturbance decoupling problem by the dynamic measurement feedback for discrete-time nonlinear control systems. To solve this problem, the algebraic approach, called the logic-dynamic approach, is used. Such an approach assumes that the system description may contain non-smooth functions. Necessary and sufficient conditions are obtained in terms of matrices similar to controlled and     ( h , f )    -invariant functions. Furthermore, procedures are developed to determine the corresponding matrices and the dynamic measurement feedback.<\/jats:p>","DOI":"10.3390\/sym11040555","type":"journal-article","created":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T11:07:11Z","timestamp":1555499231000},"page":"555","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Disturbance Decoupling Problem: Logic-Dynamic Approach-Based Solution"],"prefix":"10.3390","volume":"11","author":[{"given":"Alexey","family":"Zhirabok","sequence":"first","affiliation":[{"name":"Department of Automation and Control, Far Eastern Federal University, 690950 Vladivostok, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1109\/9.544009","article-title":"Output feedback disturbance decoupling in nonlinear systems","volume":"41","author":"Andiarti","year":"1996","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_2","unstructured":"Battilotti, S. (1997, January 10\u201312). A sufficient condition for nonlinear disturbance decoupling with stability via measurement feedback. Proceedings of the 36th Conference on Decision & Control, San Diego, CA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1109\/TAC.1981.1102604","article-title":"Nonlinear decoupling via feedback: A differential gemetric approach","volume":"26","author":"Isidori","year":"1981","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Isidori, A. (1982). The geometric approach to nonlinear feedback control: A survey. Lecture Notes in Computer and Information Science, No 4, Springer.","DOI":"10.1007\/BFb0044412"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/9.774115","article-title":"Disturbance decoupling by measurement feedback for SISO nonlinear systems","volume":"44","author":"Xia","year":"1999","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2887","DOI":"10.1016\/j.automatica.2013.06.013","article-title":"Measurement feedback disturbance decoupling in discrete-time nonlinear systems","volume":"49","author":"Kaldmae","year":"2013","journal-title":"Automatica"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1002\/asjc.1185","article-title":"Faulty plant reconfiguration based on disturbance decoupling methods","volume":"8","author":"Kaldmae","year":"2016","journal-title":"Asian J. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.nahs.2017.11.001","article-title":"Disturbance decoupling in nonlinear hybrid systems","volume":"28","author":"Kaldmae","year":"2018","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhirabok, A., and Shumsky, A. (2018). Disturbance decoupling in finite automata. Lecture Notes in Computer Science, No 10792. Language and Automata Theory and Applications, Springer.","DOI":"10.1007\/978-3-319-77313-1_9"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Conte, G., Moog, C.H., and Perdon, A.M. (2007). Algebraic Methods for Nonlinear Control Systems. Theory and Applications, Springer.","DOI":"10.1007\/978-1-84628-595-0"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"313","DOI":"10.3166\/ejc.16.313-325","article-title":"Unified approach to the problem of full decoupling via output feedback","volume":"16","author":"Shumsky","year":"2010","journal-title":"Eur. J. Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/9.557576","article-title":"On interconnections, control and feedback","volume":"42","author":"Willems","year":"1997","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"507","DOI":"10.2478\/v10006-012-0038-1","article-title":"An approach to analysis of observability and controllability in nonlinear systems via linear methods","volume":"22","author":"Zhirabok","year":"2012","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1515\/amcs-2017-0019","article-title":"Fault detection in nonlinear systems via linear methods","volume":"27","author":"Zhirabok","year":"2017","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2936","DOI":"10.1109\/TAC.2016.2604683","article-title":"Output feedback stabilization for a class of multi-variable bilinear stochastic systems with stochastic coupling attenuation","volume":"62","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/555\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:46:09Z","timestamp":1760186769000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,17]]},"references-count":15,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["sym11040555"],"URL":"https:\/\/doi.org\/10.3390\/sym11040555","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,4,17]]}}}