{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T07:05:46Z","timestamp":1775631946361,"version":"3.50.1"},"reference-count":26,"publisher":"Pleiades Publishing Ltd","issue":"1","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Autom Remote Control"],"published-print":{"date-parts":[[2018,1]]},"DOI":"10.1134\/s0005117918010083","type":"journal-article","created":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T23:50:56Z","timestamp":1517529056000},"page":"89-102","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Stochastic Stability of Some Classes of Nonlinear 2D Systems"],"prefix":"10.1134","volume":"79","author":[{"given":"P. V.","family":"Pakshin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. P.","family":"Emelianova","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. A.","family":"Emelianov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"Ga\u0142kowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"Rogers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2018,2,2]]},"reference":[{"key":"742_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TAC.1975.1100844","volume":"AC-20","author":"R.P. Roesser","year":"1975","unstructured":"Roesser, R.P., A Discrete State-Space Model for Linear Image Processing, IEEE Transact. Automat. Control, 1975, vol. AC-20, pp. 1\u201310.","journal-title":"IEEE Transact. Automat. Control"},{"key":"742_CR2","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/BF01776566","volume":"12","author":"E. Fornasini","year":"1978","unstructured":"Fornasini, E. and Marchesini, G., Doubly Indexed Dynamical Systems: State Models and Structural Properties, Math. Syst. Theory, 1978, vol. 12, pp. 59\u201372.","journal-title":"Math. Syst. Theory"},{"key":"742_CR3","volume-title":"Lecture Notes Control Inform. Sci.","author":"E. Rogers","year":"2007","unstructured":"Rogers, E., Ga\u0142kowski, K., and Owens, D.H., Control Systems Theory and Applications for Linear Repetitive Processes, Lecture Notes Control Inform. Sci., Berlin: Springer-Verlag, 2007, vol. 349."},{"key":"742_CR4","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1109\/9.186321","volume":"38","author":"J.E. Kurek","year":"1993","unstructured":"Kurek, J.E. and Zaremba, M.B., Iterative Learning Control Synthesis Based on 2D System Theory, IEEE Transact. Automat. Control, 1993, vol. 38, pp. 121\u2013125.","journal-title":"IEEE Transact. Automat. Control"},{"issue":"4","key":"742_CR5","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/j.conengprac.2009.12.003","volume":"18","author":"L. Hladowski","year":"2010","unstructured":"Hladowski, L., Ga\u0142kowski, K., Cai, Z., Rogers, E., Freeman, C.T., and Lewin, P.L., Experimentally Supported 2D Systems Based Iterative Learning Control Law Design for Error Convergence and Performance, Control Eng. Practice, 2010, vol. 18, no. 4, pp. 339\u2013348.","journal-title":"Control Eng. Practice"},{"key":"742_CR6","doi-asserted-by":"publisher","first-page":"1310","DOI":"10.1016\/j.conengprac.2013.05.011","volume":"21","author":"W. Paszke","year":"2013","unstructured":"Paszke, W., Rogers, E., Ga\u0142kowski, K., and Cai, Z., Robust Finite Frequency Range Iterative Learning Control Design and Experimental Verification, Control Eng. Practice, 2013, vol. 21, pp. 1310\u20131320.","journal-title":"Control Eng. Practice"},{"key":"742_CR7","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s00498-007-0023-7","volume":"20","author":"M. Scheicher","year":"2008","unstructured":"Scheicher, M. and Oberst, U., Multidimensional BIBO Stability and Jury\u2019s Conjecture, Math. Control, Signals, Syst., 2008, vol. 20, pp. 81\u2013109.","journal-title":"Math. Control, Signals, Syst."},{"key":"742_CR8","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1109\/81.269049","volume":"41","author":"D. Liu","year":"1994","unstructured":"Liu, D. and Michel, A.N., Stability Analysis of State-Space Realizations for Two-Dimensional Filters with Overflow Nonlinearities, IEEE Transact. Circuits Syst. I: Fundament. Theory Appl., 1994, vol. 41, pp. 127\u2013137.","journal-title":"IEEE Transact. Circuits Syst. I: Fundament. Theory Appl."},{"key":"742_CR9","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1109\/TAC.2012.2220012","volume":"58","author":"N. Yeganefar","year":"2013","unstructured":"Yeganefar, N., Yeganefar, N., Ghamgui, M., and Moulay, E., Lyapunov Theory for 2D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability, IEEE Transact. Automat. Control, 2013, vol. 58, pp. 1299\u20131304.","journal-title":"IEEE Transact. Automat. Control"},{"key":"742_CR10","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s11045-012-0193-4","volume":"25","author":"J.E. Kurek","year":"2014","unstructured":"Kurek, J.E., Stability of Nonlinear Time-Varying Digital 2D Fornasini\u2013Marchesini System, Multidimension. Syst. Signal Proc., 2014, vol. 25, pp. 235\u2013244.","journal-title":"Multidimension. Syst. Signal Proc."},{"key":"742_CR11","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.sysconle.2016.03.004","volume":"93","author":"S. Knorn","year":"2016","unstructured":"Knorn, S. and Middleton, R.H., Asymptotic and Exponential Stability of Nonlinear Two-Dimensional Continuous-Discrete Roesser Models, Syst. Control Lett., 2016, vol. 93, pp. 35\u201342.","journal-title":"Syst. Control Lett."},{"key":"742_CR12","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/S0167-6911(84)80081-X","volume":"4","author":"L. Pandolfi","year":"1984","unstructured":"Pandolfi, L., Exponential Stability of 2D Systems, Syst. Control Lett., 1984, vol. 4, pp. 381\u2013385.","journal-title":"Syst. Control Lett."},{"issue":"5","key":"742_CR13","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1134\/S000511791405004X","volume":"75","author":"J. Emelianova","year":"2014","unstructured":"Emelianova, J., Pakshin, P., Ga\u0142kowski, K., and Rogers, E., Stability of Nonlinear 2D Systems Described by the Continuous-Time Roesser Model, Autom. Remote Control, 2014, vol. 75, no. 5, pp. 845\u2013858.","journal-title":"Autom. Remote Control"},{"key":"742_CR14","first-page":"997","volume":"59","author":"G. Chesi","year":"2014","unstructured":"Chesi, G. and Middleton, R.H., Necessary and Sufficient LMI Conditions for Stability and Performance Analysis of 2D Mixed Continuous-Discrete-Time Systems, IEEE Transact. Automat. Control., 2014, vol. 59, pp. 997\u20131007.","journal-title":"IEEE Transact. Automat. Control."},{"key":"742_CR15","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.sysconle.2016.01.005","volume":"91","author":"P. Pakshin","year":"2016","unstructured":"Pakshin, P., Emelianova, J., Emelianov, M., Ga\u0142kowski, K., and Rogers, E., Dissipativity and Stabilization of Nonlinear Repetitive Processes, Syst. Control Lett., 2016, vol. 91, pp. 14\u201320.","journal-title":"Syst. Control Lett."},{"key":"742_CR16","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1134\/S1064230716040067","volume":"55","author":"K. Ga\u0142kowski","year":"2016","unstructured":"Ga\u0142kowski, K., Emelianov, M., Pakshin, P., and Rogers, E., Vector Lyapunov Functions for Stability and Stabilization of Differential Repetitive Processes, J. Comput. Syst. Sci. Int., 2016, vol. 55, pp. 503\u2013514.","journal-title":"J. Comput. Syst. Sci. Int."},{"key":"742_CR17","doi-asserted-by":"publisher","first-page":"2373","DOI":"10.1016\/j.automatica.2011.08.041","volume":"47","author":"D. Napp","year":"2011","unstructured":"Napp, D., Rapisarda, P., and Rocha, P., Time-Relevant Stability of 2D Systems, Automatica, 2011, vol. 47, pp. 2373\u20132382.","journal-title":"Automatica"},{"key":"742_CR18","first-page":"5563","volume-title":"Proc. IEEE 55 Conf. Decision Control (CDC)","author":"P. Pakshin","year":"2016","unstructured":"Pakshin, P., Emelianova, J., Emelianov, M., Ga\u0142kowski, K., and Rogers, E., Weak Stability of Nonlinear Repetitive Processes, Proc. IEEE 55 Conf. Decision Control (CDC), Las Vegas, 2016, pp. 5563\u20135568."},{"key":"742_CR19","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.sysconle.2014.12.009","volume":"75","author":"W. Paszke","year":"2015","unstructured":"Paszke, W., Dabkowski, P., Rogers, E., and Ga\u0142kowski, K., New Results on Strong Practical Stability and Stabilization of Discrete Linear Repetitive Processes, Syst. Control Lett., 2015, vol. 75, pp. 22\u201329.","journal-title":"Syst. Control Lett."},{"key":"742_CR20","first-page":"325","volume":"45","author":"J. Willems","year":"1972","unstructured":"Willems, J., Dissipative Dynamical Systems Part I: General Theory, Arch. Rational Mech. Anal., 1972, vol. 45, pp. 325\u2013351.","journal-title":"Arch. Rational Mech. Anal."},{"key":"742_CR21","doi-asserted-by":"publisher","first-page":"1228","DOI":"10.1109\/9.100932","volume":"36","author":"C. Byrnes","year":"1991","unstructured":"Byrnes, C., Isidori, A., and Willems, J., Passivity, Feedback Equivalence and the Global Stabilization of Minimun Phase Nonlinear Systems, IEEE Transact. Autom. Control, 1991, vol. 36, pp. 1228\u20131240.","journal-title":"IEEE Transact. Autom. Control"},{"key":"742_CR22","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1109\/9.928588","volume":"46","author":"S.S. Saab","year":"2001","unstructured":"Saab, S.S., A Discrete-Time Stochastic Learning Control Algorithm, IEEE Transact. Autom. Control, 2001, vol. 46, pp. 877\u2013887.","journal-title":"IEEE Transact. Autom. Control"},{"key":"742_CR23","first-page":"1864","volume-title":"Proc. IEEE 54 Conf. Decision and Control (CDC)","author":"P. Pakshin","year":"2015","unstructured":"Pakshin, P., Emelianova, J., Emelianov, M., Ga\u0142kowski, K., and Rogers, E., Stability of Stochastic Repetitive Processes, Proc. IEEE 54 Conf. Decision and Control (CDC), Osaka, 2015, pp. 1864\u20131869."},{"issue":"3","key":"742_CR24","doi-asserted-by":"publisher","first-page":"8247","DOI":"10.3182\/20140824-6-ZA-1003.00729","volume":"47","author":"J. Emelianova","year":"2014","unstructured":"Emelianova, J., Pakshin, P., Ga\u0142kowski, K., and Rogers, E., Vector Lyapunov Function Based Stability of a Class of Applications Relevant 2D Nonlinear Systems, IFAC Proc. Volumes (IFAC-PapersOnline), 2014, vol. 47, no. 3, pp. 8247\u20138252.","journal-title":"IFAC Proc. Volumes (IFAC-PapersOnline)"},{"issue":"10","key":"742_CR25","doi-asserted-by":"publisher","first-page":"1852","DOI":"10.1134\/S0005117907100128","volume":"68","author":"P.V. Pakshin","year":"2007","unstructured":"Pakshin, P.V., Exponential Dissipativeness of the Random-structure Diffussion Processes and Problems of Robust Stabilization, Autom. Remote Control, 2007, vol. 68, no. 10, pp. 1852\u20131870.","journal-title":"Autom. Remote Control"},{"key":"742_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-23280-0","volume-title":"Stochastic Stability of Differential Equations","author":"R. Khasminskii","year":"2012","unstructured":"Khasminskii, R., Stochastic Stability of Differential Equations, Berlin: Springer-Verlag, 2012."}],"container-title":["Automation and Remote Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0005117918010083","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117918010083.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117918010083.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:38:35Z","timestamp":1773614315000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0005117918010083"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["742"],"URL":"https:\/\/doi.org\/10.1134\/s0005117918010083","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"value":"0005-1179","type":"print"},{"value":"1608-3032","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]},"assertion":[{"value":"20 March 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 February 2018","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}