{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:18:45Z","timestamp":1773656325396,"version":"3.50.1"},"reference-count":34,"publisher":"Pleiades Publishing Ltd","issue":"1","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"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":[[2016,1]]},"DOI":"10.1134\/s000511791601001x","type":"journal-article","created":{"date-parts":[[2016,1,20]],"date-time":"2016-01-20T11:04:13Z","timestamp":1453287853000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Suboptimal anisotropic filtering in a finite horizon"],"prefix":"10.1134","volume":"77","author":[{"given":"V. N.","family":"Timin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. P.","family":"Kurdyukov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2016,1,21]]},"reference":[{"key":"385_CR1","first-page":"34","volume":"82D","author":"R. Kalman","year":"1960","unstructured":"Kalman, R., A New Approach to Linear Filtering and Prediction Problems, Trans. ASME. J. Basic Eng., 1960, vol. 82D, pp. 34\u201345.","journal-title":"Trans. ASME. J. Basic Eng."},{"key":"385_CR2","volume-title":"Optimal Filtering","author":"B.D.O. Anderson","year":"1979","unstructured":"Anderson, B.D.O. and Moore, J.B., Optimal Filtering, Englewood Cliffs: Prentice Hall, 1979."},{"key":"385_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970760","volume-title":"Indefinite Quadratic Estimation and Control: A Unified Approach to H 2 and H \u221e Theories","author":"B. Hassibi","year":"1999","unstructured":"Hassibi, B., Sayed, A., and Kailath, T., Indefinite Quadratic Estimation and Control: A Unified Approach to H\n                                    2\n                                    and H\n                                    \u221e\n                                    Theories, Philadelphia: SIAM, 1999."},{"issue":"4","key":"385_CR4","doi-asserted-by":"publisher","first-page":"756","DOI":"10.1109\/TAC.1978.1101812","volume":"AC-23","author":"J.C. Doyle","year":"1978","unstructured":"Doyle, J.C., Guaranteed Margins for LQG Regulators, IEEE Trans. Automat. Control, 1978, vol. AC-23, no. 4, pp. 756\u2013757.","journal-title":"IEEE Trans. Automat. Control"},{"key":"385_CR5","doi-asserted-by":"publisher","DOI":"10.1002\/0470045345","volume-title":"Optimal State Estimation: Kalman, Infinity, and Nonlinear Approaches","author":"D. Simon","year":"2006","unstructured":"Simon, D., Optimal State Estimation: Kalman, Infinity, and Nonlinear Approaches, New Jersey: Wiley, 2006."},{"issue":"2","key":"385_CR6","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1109\/9.67291","volume":"36","author":"K.M. Nagpal","year":"1991","unstructured":"Nagpal, K.M. and Khargonekar, P.P., Filtering and Smoothing in an H\n                                    \u221e-setting, IEEE Trans. Automat. Control, 1991, vol. 36, no. 2, pp. 152\u2013166.","journal-title":"IEEE Trans. Automat. Control"},{"key":"385_CR7","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1109\/29.57538","volume":"38","author":"M.J. Grimble","year":"1990","unstructured":"Grimble, M.J. and Elsayed, A., Solution of the H\n                                    \u221e Optimal Linear Filtering Problem for Discrete-time Systems, IEEE Trans. Acoust. Speech Signal Proc., 1990, vol. 38, pp. 1092\u20131104.","journal-title":"IEEE Trans. Acoust. Speech Signal Proc."},{"key":"385_CR8","first-page":"2278","volume-title":"Proc. 31 IEEE CDC","author":"U. Shaked","year":"1992","unstructured":"Shaked, U. and Theodor, Y., H\n                                    \u221e-optimal Estimation: A Tutorial, in Proc. 31 IEEE CDC, 1992, pp. 2278\u20132286."},{"key":"385_CR9","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1109\/78.286964","volume":"42","author":"Y. Theodor","year":"1994","unstructured":"Theodor, Y., Shaked, U., and de Souza, C.E., A Game Theory Approach to Robust Discrete-time H\n                                    \u221e Estimation, IEEE Trans. Signal Proc., 1994, vol. 42, pp. 1486\u20131495.","journal-title":"IEEE Trans. Signal Proc."},{"key":"385_CR10","doi-asserted-by":"publisher","first-page":"1564","DOI":"10.1109\/9.310030","volume":"39","author":"K. Zhou","year":"1994","unstructured":"Zhou, K., Glover, K., Bodenheimer, B., and Doyle, J., Mixed H\n                                    2 and H\n                                    \u221e Performance Objectives I: Robust Performance Analysis, IEEE Trans. Automat. Control, 1994, vol. 39, pp. 1564\u20131574.","journal-title":"IEEE Trans. Automat. Control"},{"key":"385_CR11","doi-asserted-by":"publisher","first-page":"1575","DOI":"10.1109\/9.310031","volume":"39","author":"J. Doyle","year":"1994","unstructured":"Doyle, J., Zhou, K., Gover, K., and Bodenheimer, B., Mixed H\n                                    2 and H\n                                    \u221e Performance Objectives II: Optimal Control, IEEE Trans. Automat. Control, 1994, vol. 39, pp. 1575\u20131587.","journal-title":"IEEE Trans. Automat. Control"},{"key":"385_CR12","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BFb0114643","volume-title":"Proc. Workshop on Robust Control","author":"D.J.N. Limebeer","year":"1992","unstructured":"Limebeer, D.J.N., Anderson, B.D.O., and Hendel, B., Mixed H\n                                    2\/H\n                                    \u221e Filtering by the Theory of Nash Games, in Proc. Workshop on Robust Control, Tokyo, Japan, 1992, pp. 9\u201315."},{"issue":"4","key":"385_CR13","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/0167-6911(91)90011-3","volume":"16","author":"W.M. Haddad","year":"1991","unstructured":"Haddad, W.M., Bernstein, D.S., and Mustafa, D., Mixed-norm H\n                                    2\/H\n                                    \u221e Regulation and Estimation: The Discrete-time Case, Syst. Control Lett., 1991, vol. 16, no. 4, pp. 235\u2013247.","journal-title":"Syst. Control Lett."},{"key":"385_CR14","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1002\/(SICI)1099-1239(199605)6:4<313::AID-RNC235>3.0.CO;2-8","volume":"6","author":"P.P. Khargonekar","year":"1996","unstructured":"Khargonekar, P.P., Rotea, M.A., and Baeyens, E., Mixed H\n                                    2\/H\n                                    \u221e Filtering, Int. J. Robust Nonlin. Control, 1996, vol. 6, pp. 313\u2013330.","journal-title":"Int. J. Robust Nonlin. Control"},{"issue":"9","key":"385_CR15","doi-asserted-by":"publisher","first-page":"2338","DOI":"10.1109\/78.622956","volume":"45","author":"L. Huaizhong","year":"1997","unstructured":"Huaizhong, Li and Minyue, Fu, A Linear Matrix Inequality Approach to Robust H\n                                    \u221e Filtering, IEEE Trans. Signal Proc., 1997, vol. 45, no. 9, pp. 2338\u20132350.","journal-title":"IEEE Trans. Signal Proc."},{"key":"385_CR16","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970777","volume-title":"Linear Matrix Inequalities in System and Control Theory","author":"S. Boyd","year":"1994","unstructured":"Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994."},{"key":"385_CR17","doi-asserted-by":"crossref","unstructured":"Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of the Control Laws on the Basis of Matrix Linear Inequalities), Moscow: Fizmatlit, 2007.","DOI":"10.1134\/S0005117907030010"},{"issue":"11","key":"385_CR18","first-page":"1507","volume":"48","author":"D.V. Balandin","year":"2012","unstructured":"Balandin, D.V. and Kogan, M.M., Generalized H\n                                    \u221e-optimal Filtering under External and Initial Disturbances, Differ. Uravn., 2012, vol. 48, no. 11, pp. 1507\u20131514.","journal-title":"Differ. Uravn."},{"key":"385_CR19","doi-asserted-by":"publisher","first-page":"1216","DOI":"10.1080\/00207179.2013.873543","volume":"87","author":"M.M. Kogan","year":"2014","unstructured":"Kogan, M.M., LMI Based Minimax Estimation and Filtering under Unknown Covariances, Int. J. Control, 2014, vol. 87, pp. 1216\u20131226.","journal-title":"Int. J. Control"},{"key":"385_CR20","volume-title":"H \u221e Control and Estimation of State-Multiplicative Linear Systems","author":"E. Gershon","year":"2005","unstructured":"Gershon, E., Shaked, U., and Yaesh, I., H\n                                    \u221e\n                                    Control and Estimation of State-Multiplicative Linear Systems, London: Springer, 2005."},{"issue":"1","key":"385_CR21","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1080\/00207170150202661","volume":"74","author":"P. Diamond","year":"2001","unstructured":"Diamond, P., Vladimirov, I., Kurdjukov, A., and Semyonov, A., Anisotropy-based Perfomance Analysis of Linear Discrete Time Invariant Control Systems, Int. J. Control, 2001, vol. 74, no. 1, pp. 28\u201342.","journal-title":"Int. J. Control"},{"key":"385_CR22","volume-title":"Anisotropy-based Optimal Filtering in Linear Discrete Time Invariant Systems","author":"I. Vladimirov","year":"2012","unstructured":"Vladimirov, I., Anisotropy-based Optimal Filtering in Linear Discrete Time Invariant Systems, 2012 http:\/\/arxiv.org\/abs\/1412.3010."},{"key":"385_CR23","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1134\/S1064562412030362","volume":"85","author":"V.N. Timin","year":"2012","unstructured":"Timin, V.N., Tchaikovsky, M.M., and Kurdyukov, A.P., A Solution to Anisotropic Suboptimal Filtering Problem by Convex Optimization, Dokl. Math., 2012, vol. 85, pp. 443\u2013445.","journal-title":"Dokl. Math."},{"issue":"11","key":"385_CR24","doi-asserted-by":"publisher","first-page":"1773","DOI":"10.1134\/S0005117913110015","volume":"74","author":"V.N. Timin","year":"2013","unstructured":"Timin, V.N., Anisotropy-based Suboptimal Filtering for the Linear Discrete Time-invariant Systems, Autom. Remote Control, 2013, vol. 74, no. 11, pp. 1773\u20131785.","journal-title":"Autom. Remote Control"},{"issue":"8","key":"385_CR25","doi-asserted-by":"publisher","first-page":"1265","DOI":"10.1134\/S0005117906080066","volume":"67","author":"I.G. Vladimirov","year":"2006","unstructured":"Vladimirov, I.G., Diamond, P., and Kloeden, P., Anisotropy-based Robust Performance Analysis of Finite Horizon Linear Discrete Time Varying Systems, Autom. Remote Control, 2006, vol. 67, no. 8, pp. 1265\u20131282.","journal-title":"Autom. Remote Control"},{"key":"385_CR26","volume-title":"Univ. of Queensland","author":"I. Vladimirov","year":"2001","unstructured":"Vladimirov, I. and Diamond, P., Robust Filtering in Finite Horizon Linear Discrete Time Varying Systems by Minimum Anisotropic Norm Criterion, CADSMAP Research Report 01-05, Center for Applied Dynamical Systems\/Center for Applied Dynamical Systems, Mathematical Analysis and Probability, Univ. of Queensland, Brisbane, Australia, 2001."},{"key":"385_CR27","first-page":"4701","volume-title":"Milano","author":"E.A. Maximov","year":"2011","unstructured":"Maximov, E.A., Kurdyukov, A.P., and Vladimirov, I.G., Anisotropic Norm Bounded Real Lemma for Linear Time-varying System, in Preprint 18 IFAC World Congr., Milano, 2011, pp. 4701\u20134706."},{"key":"385_CR28","first-page":"975","volume-title":"Proc. Eur. Control Conf., Strasbourg","author":"I. Yaesh","year":"2014","unstructured":"Yaesh, I. and Stoica, A.-M., Linear Time-varying Anisotropic Filtering its Application to Nonlinear Systems State Estimation, in Proc. Eur. Control Conf., Strasbourg, 2014, June 24\u201327, pp. 975\u2013980."},{"key":"385_CR29","doi-asserted-by":"publisher","DOI":"10.1002\/0471200611","volume-title":"Elements of Information Theory","author":"T.M. Cover","year":"1991","unstructured":"Cover, T.M. and Thomas, J.A., Elements of Information Theory, New York: Wiley, 1991."},{"key":"385_CR30","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718829","volume-title":"Lectures on Modern Convex Optimization. MPS-SIAM Series on Optimization","author":"A. Ben-Tal","year":"2001","unstructured":"Ben-Tal, A. and Nemirovski, A., Lectures on Modern Convex Optimization. MPS-SIAM Series on Optimization, Philadelphia: SIAM, 2001."},{"key":"385_CR31","first-page":"421","volume-title":"Proc. 28 Conf. Decision Control","author":"I. Yaesh","year":"1989","unstructured":"Yaesh, I. and Shaked, U., Game Theory Approach to Optimal Linear Estimation in Minimum H\n                                    \u221e-norm Sense, in Proc. 28 Conf. Decision Control, Tampa, Florida, December 1989, pp. 421\u2013425."},{"key":"385_CR32","volume-title":"Proc. CACSD Conf., Taipei, Taiwan","author":"J. Lofberg","year":"2004","unstructured":"Lofberg, J., YALMIP: A Toolbox for Modeling and Optimization in MATLAB, in Proc. CACSD Conf., Taipei, Taiwan, 2004, http:\/\/users.isy.liu.se\/johanl\/yalmip\/."},{"key":"385_CR33","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"J.F. Sturm","year":"1999","unstructured":"Sturm, J.F., Using SeDuMi 1.02, a MATLAB Toolbox for Optimization over Symmetric Cones, Optim. Methods Software, 1999, vol. 11, pp. 625\u2013653.","journal-title":"Optim. Methods Software"},{"key":"385_CR34","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/S0024-3795(98)10166-0","volume":"286","author":"G. Freiling","year":"1999","unstructured":"Freiling, G. and Ionescu, V., Time-varing Discrete Riccati Equation: Some Monotonicity Resuits, Linear Algebra Appl., 1999, vol. 286, pp. 135\u2013148.","journal-title":"Linear Algebra Appl."}],"container-title":["Automation and Remote Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S000511791601001X.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S000511791601001X","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S000511791601001X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S000511791601001X.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:25:08Z","timestamp":1773613508000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S000511791601001X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["385"],"URL":"https:\/\/doi.org\/10.1134\/s000511791601001x","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"value":"0005-1179","type":"print"},{"value":"1608-3032","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1]]},"assertion":[{"value":"30 March 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2016","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}