{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:19:43Z","timestamp":1773656383790,"version":"3.50.1"},"reference-count":26,"publisher":"Pleiades Publishing Ltd","issue":"1","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"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":[[2019,1]]},"DOI":"10.1134\/s0005117919010016","type":"journal-article","created":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T13:40:54Z","timestamp":1554298854000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Suboptimal Anisotropic Filtering for Linear Discrete Nonstationary Systems with Uncentered External Disturbance"],"prefix":"10.1134","volume":"80","author":[{"given":"V. N.","family":"Timin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. Yu.","family":"Kustov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. P.","family":"Kurdyukov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D. A.","family":"Goldin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu. A.","family":"Vershinin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"906_CR1","volume-title":"Optimal Filtering","author":"B.D.O. Anderson","year":"1979","unstructured":"Anderson, B.D.O. and Moore, J.B., Optimal Filtering, New Jersey: Prentice Hall, 1979."},{"key":"906_CR2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970760","volume-title":"Indefinite Quadratic Estimation and Control: A Unified Approach to H2 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 H2 and H\u221e Theories, Philadelphia: SIAM, 1999."},{"key":"906_CR3","doi-asserted-by":"publisher","DOI":"10.1002\/0470045345","volume-title":"Optimal State Estimation: Kalman, H\u221e, and Nonlinear Approaches","author":"D. Simon","year":"2006","unstructured":"Simon, D., Optimal State Estimation: Kalman, H\u221e, and Nonlinear Approaches, New Jersey: Wiley, 2006."},{"key":"906_CR4","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 H2 and H\u221e Performance Objectives I: Robust Performance Analysis, IEEE Trans. Automat. Control, 1994, vol. 39, pp. 1564\u20131574.","journal-title":"IEEE Trans. Automat. Control"},{"issue":"4","key":"906_CR5","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 H2\/H\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":"906_CR6","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 H2\/H\u221e Filtering, Int. J. Robust Nonlin. Control, 1996, vol. 6, pp. 313\u2013330.","journal-title":"Int. J. Robust Nonlin. Control"},{"key":"906_CR7","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0167-6911(89)90089-3","volume":"12","author":"D.S. Bernstein","year":"1989","unstructured":"Bernstein, D.S. and Haddad, W.M., Steady-State Kalman Filtering with an H\u221e Error Bound, Syst. Control Lett., 1989, vol. 12, pp. 9\u201316.","journal-title":"Syst. Control Lett."},{"key":"906_CR8","volume-title":"Tokyo, Japan","author":"D.J.N. Limebeer","year":"1992","unstructured":"Limebeer, D.J.N., Anderson, B.D.O., and Hendel, B., Mixed H2\/H\u221e Filtering by the Theory of Nash Games, Proc. Workshop Robust Control, Tokyo, Japan, 1992, pp. 9\u201315."},{"issue":"9","key":"906_CR9","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\u221e Filtering, IEEE Trans. Signal Proc., 1997, vol. 45, no. 9, pp. 2338\u20132350.","journal-title":"Signal Proc."},{"key":"906_CR10","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1109\/9.763229","volume":"44","author":"Z. Wang","year":"1999","unstructured":"Wang, Z. and Unbehauen, H., Robust H2\/H\u221e State Estimation for Systems with Error Variance Constraints: The Continuous-Time Case, IEEE Trans. Automat. Control, 1999, vol. 44, pp. 1061\u20131065.","journal-title":"IEEE Trans. Automat. Control"},{"issue":"1","key":"906_CR11","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1109\/7.913689","volume":"37","author":"R.M. Palhares","year":"2001","unstructured":"Palhares, R.M. and Peres, P.L.D., LMI Approach to the Mixed H2\/H\u221e Filtering Design for Discrete-Time Uncertain Systems, IEEE Trans. Aerospace Electron. Syst., 2001, vol. 37, no. 1, pp. 292\u2013296.","journal-title":"IEEE Trans. Aerospace Electron. Syst."},{"key":"906_CR12","volume-title":"Proc. 33 IEEE Conf. Decision Control, Florida, USA","author":"A.V. Semyonov","year":"1994","unstructured":"Semyonov, A.V., Vladimirov, I.G., and Kurdjukov, A.P., Stochastic Approach to H\u221e-optimization, Proc. 33 IEEE Conf. Decision Control, Florida, USA, 1994, pp. 2249\u20132250."},{"issue":"5","key":"906_CR13","first-page":"607","volume":"343","author":"I.G. Vladimirov","year":"1995","unstructured":"Vladimirov, I.G., Kurdyukov, A.P., and Semenov, A.V., A Stochastic H\u221e-Optimization Problem, Dokl. Mat., 1995, vol. 343, no. 5, pp. 607\u2013609.","journal-title":"Dokl. Mat."},{"issue":"5","key":"906_CR14","first-page":"583","volume":"342","author":"I.G. Vladimirov","year":"1995","unstructured":"Vladimirov, I.G., Kurdyukov, A.P., and Semenov, A.V., Anisotropy of Signals and Entropy of Linear Stationary Systems, Dokl. Mat., 1995, vol. 342, no. 5, pp. 583\u2013585.","journal-title":"Dokl. Mat."},{"key":"906_CR15","volume-title":"Proc. 13 IFAC World Congr., San-Francisco, June 30\u2013July 5","author":"I.G. Vladimirov","year":"1996","unstructured":"Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., On Computing the Anisotropic Norm of Linear Discrete-Time-Invariant Systems, Proc. 13 IFAC World Congr., San-Francisco, June 30\u2013July 5, 1996."},{"key":"906_CR16","volume-title":"Proc. 13 IFAC World Congr., San-Francisco","author":"I.G. Vladimirov","year":"1996","unstructured":"Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., State-Space Solution to Anisotropy-Based Stochastic H\u221e-Optimization Problem, Proc. 13 IFAC World Congr., San-Francisco, 1996, pp. 427\u2013432."},{"key":"906_CR17","volume-title":"Anisotropy-Based Optimal Filtering in Linear Discrete Time Invariant Systems, CADSMAP Res. Report 01-03","author":"I.G. Vladimirov","year":"2001","unstructured":"Vladimirov, I.G., Anisotropy-Based Optimal Filtering in Linear Discrete Time Invariant Systems, CADSMAP Res. Report 01-03, 2001, arXiv: 1412.3010 [completed in 2001]."},{"issue":"8","key":"906_CR18","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"},{"issue":"6","key":"906_CR19","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1134\/S0005117917060029","volume":"78","author":"A.Yu. Kustov","year":"2017","unstructured":"Kustov, A.Yu. and Timin, V.N., Anisotropy-Based Analysis for Finite Horizon Time-Varying Systems with Non-Centered Disturbances, Autom. Remote Control, 2017, vol. 78, no. 6, pp. 974\u2013988.","journal-title":"Autom. Remote Control"},{"key":"906_CR20","volume-title":"Robust Filtering in Finite Horizon Linear Discrete Time Varying Systems by Minimum Anisotropic Norm Criterion","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 Res. Report 01\u201305, 2001 [completed in 2001]."},{"key":"906_CR21","volume-title":"Anisotropic Norm Bounded Real Lemma for Linear Time-Varying System, Preprint 18th IFAC World Congr.","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, Preprint 18th IFAC World Congr., Milano, 2011, pp. 4701\u20134706."},{"key":"906_CR22","volume-title":"Proc. Eur. Control Conf., Strasburg","author":"I. Yaesh","year":"2014","unstructured":"Yaesh, I. and Stoica, A.-M., Linear Time-Varying Anisotropic Filtering Its Application to Nonlinear Systems State Estimation, Proc. Eur. Control Conf., Strasburg, 2014, June 24\u201327, pp. 975\u2013980."},{"issue":"1","key":"906_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1134\/S000511791601001X","volume":"77","author":"V.N. Timin","year":"2016","unstructured":"Timin, V.N. and Kurdyukov, A.P., Suboptimal Anisotropic Filtering in a Finite Horizon, Autom. Remote Control, 2016, vol. 77, no. 1, pp. 1\u201320.","journal-title":"Autom. Remote Control"},{"key":"906_CR24","volume-title":"Proc. 13th IFAC World Congr., Toulouse, France, July 9\u201314","author":"A.Yu. Kustov","year":"2017","unstructured":"Kustov, A.Yu. and Timin, V.N., Suboptimal Anisotropy-based Control for Linear Discrete Time Varying Systems with Noncentered Disturbances, Proc. 13th IFAC World Congr., Toulouse, France, July 9\u201314, 2017, pp. 6296\u20136301."},{"key":"906_CR25","volume-title":"YALMIP: A Toolbox for Modeling and Optimization in MATLA","author":"J. Lofberg","year":"2004","unstructured":"Lofberg, J., YALMIP: A Toolbox for Modeling and Optimization in MATLAB, Proc. CACSD Conf., Taipei, Taiwan, 2004. http:\/\/users.isy.liu.se\/johanl\/yalmip\/"},{"key":"906_CR26","first-page":"625","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":"Using SeDuMi 1.02, A MATLAB Toolbox for Optimization Over Symmetric Cones, Optim. Methods Software"}],"container-title":["Automation and Remote Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117919010016.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0005117919010016","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117919010016.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:33:18Z","timestamp":1773613998000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0005117919010016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["906"],"URL":"https:\/\/doi.org\/10.1134\/s0005117919010016","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"value":"0005-1179","type":"print"},{"value":"1608-3032","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"29 December 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 November 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}