{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T15:21:58Z","timestamp":1764688918043,"version":"3.40.4"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2013,1,4]],"date-time":"2013-01-04T00:00:00Z","timestamp":1357257600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2013,12]]},"DOI":"10.1007\/s10898-012-0027-9","type":"journal-article","created":{"date-parts":[[2013,1,3]],"date-time":"2013-01-03T09:33:14Z","timestamp":1357205594000},"page":"1245-1262","source":"Crossref","is-referenced-by-count":20,"title":["Infinite horizon $$H_2\/H_\\infty $$ optimal control for discrete-time Markov jump systems with ( $$x,u,v$$ )-dependent noise"],"prefix":"10.1007","volume":"57","author":[{"given":"Ting","family":"Hou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weihai","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongji","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,1,4]]},"reference":[{"key":"27_CR1","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/2946.001.0001","volume-title":"The Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications","author":"N Weiner","year":"1949","unstructured":"Weiner, N.: The Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications. Weiley, New York (1949)"},{"issue":"1","key":"27_CR2","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1115\/1.3662552","volume":"82","author":"RE Kalman","year":"1960","unstructured":"Kalman, R.E.: A new approach to linear filtering and prediction problems. ASME J. Basic Eng. 82(1), 34\u201345 (1960)","journal-title":"ASME J. Basic Eng."},{"key":"27_CR3","unstructured":"Kalman, R.E.: On the general theory of control systems. IFAC First International Conference, pp. 481\u2013493 (1960)"},{"key":"27_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03620-4","volume-title":"Stochastic Differential Equations: An Introduction with Application","author":"B Oksendal","year":"1998","unstructured":"Oksendal, B.: Stochastic Differential Equations: An Introduction with Application, 5th edn. Springer, New York (1998)","edition":"5"},{"key":"27_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/b138575","volume-title":"Discrete-Time Markovian Jump Linear Systems","author":"OLV Costa","year":"2005","unstructured":"Costa, O.L.V., Fragoso, M.D., Marques, R.P.: Discrete-Time Markovian Jump Linear Systems. Springer, New York (2005)"},{"key":"27_CR6","volume-title":"Control of Singular Systems with Random Abrupt Changes","author":"EK Boukas","year":"2008","unstructured":"Boukas, E.K.: Control of Singular Systems with Random Abrupt Changes. Springer, Berlin (2008)"},{"key":"27_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1466-3","volume-title":"Stochastic Control: Hamilton Sytsems and HJB Equations","author":"J Yong","year":"1999","unstructured":"Yong, J., Zhou, X.Y.: Stochastic Control: Hamilton Sytsems and HJB Equations. Springer, New York (1999)"},{"issue":"7","key":"27_CR8","doi-asserted-by":"crossref","first-page":"1630","DOI":"10.1109\/TAC.2008.929368","volume":"53","author":"W Zhang","year":"2008","unstructured":"Zhang, W., Zhang, H., Chen, B.S.: Generalized Lyapunov equation approach to state-dependent stochastic stabilization\/detectability criterion. IEEE Trans. Autom. Control 53(7), 1630\u20131642 (2008)","journal-title":"IEEE Trans. Autom. Control"},{"key":"27_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-0447-6","volume-title":"Robust Control Design Using $$H_\\infty $$ Methods","author":"IR Petersen","year":"2000","unstructured":"Petersen, I.R., Ugrinovskii, V., Savkin, A.V.: Robust Control Design Using $$H_\\infty $$ Methods. Springer, Berlin (2000)"},{"issue":"7","key":"27_CR10","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1109\/TAC.2010.2047033","volume":"55","author":"Z Wang","year":"2010","unstructured":"Wang, Z., Ho, D.W.C., Dong, H., Gao, H.: Robust $$H_{\\infty }$$ finite horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations. IEEE Trans. Autom. Control 55(7), 1716\u20131722 (2010)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"27_CR11","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/TAC.1981.1102603","volume":"26","author":"G Zames","year":"1981","unstructured":"Zames, G.: Feedback and optimal sensitivity: Model reference transformation, multiplicative seminorms, and approximative inverses. IEEE Trans. Autom. Control 26(2), 301\u2013320 (1981)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"8","key":"27_CR12","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1109\/9.29425","volume":"34","author":"JC Doyle","year":"1989","unstructured":"Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.: State-space solutions to standard $$H_{2}$$ and $$H_{\\infty }$$ problems. IEEE Trans. Autom. Control 34(8), 831\u2013847 (1989)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"1","key":"27_CR13","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/9.273340","volume":"39","author":"DJN Limebeer","year":"1994","unstructured":"Limebeer, D.J.N., Anderson, B.D.O., Hendel, B.: A Nash game approach to mixed $$H_2\/H_{\\infty }$$ control. IEEE Trans. Autom. Control 39(1), 69\u201382 (1994)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"7","key":"27_CR14","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1109\/9.85062","volume":"36","author":"PP Khargonekar","year":"1991","unstructured":"Khargonekar, P.P., Rotea, M.A.: Mixed $$H_2\/H_{\\infty }$$ control: a convex optimization approach. IEEE Trans. Autom. Control 36(7), 824\u2013837 (1991)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"5","key":"27_CR15","doi-asserted-by":"crossref","first-page":"1504","DOI":"10.1137\/S0363012996301336","volume":"36","author":"D Hinrichsen","year":"1998","unstructured":"Hinrichsen, D., Pritchard, A.J.: Stochastic $$H_{\\infty }$$ . SIAM J. Control Optim. 36(5), 1504\u20131538 (1998)","journal-title":"SIAM J. Control Optim."},{"issue":"6","key":"27_CR16","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1137\/S0363012903423727","volume":"44","author":"W Zhang","year":"2006","unstructured":"Zhang, W., Chen, B.S.: State feedback $$H_{\\infty }$$ control for a class of nonlinear stochastic systems. SIAM J. Control Optim. 44(6), 1973\u20131991 (2006)","journal-title":"SIAM J. Control Optim."},{"issue":"3","key":"27_CR17","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/TAC.2004.824479","volume":"49","author":"G Yin","year":"2004","unstructured":"Yin, G., Zhou, X.Y.: Markowitz\u2019s mean-variance portfolio selection with regime switching: from discrete-time models to their continuous-time limits. IEEE Trans. Autom. Control 49(3), 349\u2013360 (2004)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"27_CR18","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1023\/A:1024887007165","volume":"27","author":"X Li","year":"2003","unstructured":"Li, X., Zhou, X.Y., Ait Rami, M.: Indefinite stochastic linear quadratic control with Markovian jumps in infinite time horizon. J. Glob. Optim. 27(2), 149\u2013175 (2003)","journal-title":"J. Glob. Optim."},{"key":"27_CR19","doi-asserted-by":"crossref","DOI":"10.1142\/p473","volume-title":"Stochastic Differential Equations with Markovian Swithcing","author":"X Mao","year":"2006","unstructured":"Mao, X., Yuan, C.: Stochastic Differential Equations with Markovian Swithcing. Imperial College Press, London (2006)"},{"key":"27_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-0630-4","volume-title":"Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems","author":"V Dragan","year":"2010","unstructured":"Dragan, V., Morozan, T., Stoica, A.M.: Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems. Springer, New York (2010)"},{"issue":"12","key":"27_CR21","doi-asserted-by":"crossref","first-page":"2955","DOI":"10.1016\/j.automatica.2009.09.027","volume":"45","author":"Z Lin","year":"2009","unstructured":"Lin, Z., Lin, Y., Zhang, W.: A unified design for state and output feedback $$H_{\\infty }$$ control of nonlinear stochastic Markov jump systems with state and disturbance-dependent noise. Automatica 45(12), 2955\u20132962 (2009)","journal-title":"Automatica"},{"issue":"2","key":"27_CR22","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/TMECH.2008.2009442","volume":"14","author":"AAG Siqueria","year":"2009","unstructured":"Siqueria, A.A.G., Terra, M.H.: A fault-tolerant manipulator robot based on $$H_{2}, H_{\\infty }$$ and $$H_2\/H_{\\infty }$$ Markov controls. IEEE Trans. Mechatron. 14(2), 257\u2013263 (2009)","journal-title":"IEEE Trans. Mechatron."},{"issue":"3","key":"27_CR23","doi-asserted-by":"crossref","first-page":"2306","DOI":"10.1016\/j.automatica.2008.01.028","volume":"44","author":"W Zhang","year":"2008","unstructured":"Zhang, W., Huang, Y., Xie, L.: Infinite horizon stochastic $$H_{2}\/H_{\\infty }$$ control for discrete-time systems with state and disturbance dependent noise. Automatica 44(3), 2306\u20132316 (2008)","journal-title":"Automatica"},{"issue":"5","key":"27_CR24","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/TAC.2010.2041987","volume":"55","author":"T Hou","year":"2010","unstructured":"Hou, T., Zhang, W., Ma, H.: Finite horizon $$H_2\/H_\\infty $$ control for discrete-time stochastic systems with Markovian jumps and multiplicative noise. IEEE Trans. Autom. Control 55(5), 1185\u20131191 (2010)","journal-title":"IEEE Trans. Autom. Control"},{"key":"27_CR25","unstructured":"Hou, T.: Stability and Robust $$H_2\/H_\\infty $$ Control for Discrete-Time Markov Jump Systems. Ph.D. thesis, Shandong University of Science and Technology, Qingdao, China (2010)"},{"key":"27_CR26","first-page":"771","volume":"9","author":"T Morozan","year":"1993","unstructured":"Morozan, T.: Stochastic uniformly observability and Riccati equations of stochastic control. Revue Roumaine de Math\u00e9matique Pures et Appliqu\u00e9es 9, 771\u2013781 (1993)","journal-title":"Revue Roumaine de Math\u00e9matique Pures et Appliqu\u00e9es"},{"key":"27_CR27","doi-asserted-by":"crossref","unstructured":"Ma H., Zhang W., Hou, T.: Infinite horizon $$H_2\/H_\\infty $$ control for discrete-time time-varying Markov jump systems with multiplicative noise. The 18th IFAC World Congress, Milano, Italy, pp. 4626\u20134631 (2011)","DOI":"10.3182\/20110828-6-IT-1002.02412"},{"issue":"1","key":"27_CR28","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01397969","volume":"7","author":"H Schneider","year":"1965","unstructured":"Schneider, H.: Positive operator and an inertia theorem. Numer. Math. 7(1), 11\u201317 (1965)","journal-title":"Numer. Math."},{"issue":"2","key":"27_CR29","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0167-6911(01)00134-7","volume":"44","author":"EF Costa","year":"2001","unstructured":"Costa, E.F., do Val, J.B.R.: On the detectability and observability of discrete-time Markov jump linear systems. Syst. Control Lett. 44(2), 135\u2013145 (2001)","journal-title":"Syst. Control Lett."},{"issue":"1","key":"27_CR30","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1007\/s11424-010-9270-7","volume":"23","author":"Y Ni","year":"2010","unstructured":"Ni, Y., Zhang, W., Fang, H.: On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise. J. Syst. Sci. Complex. 23(1), 102\u2013115 (2010)","journal-title":"J. Syst. Sci. Complex."},{"issue":"1","key":"27_CR31","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/TAC.2003.821400","volume":"49","author":"BS Chen","year":"2004","unstructured":"Chen, B.S., Zhang, W.: Stochastic $$H_{2}\/H_{\\infty }$$ control with state-dependent noise. IEEE Trans. Autom. Control 49(1), 45\u201357 (2004)","journal-title":"IEEE Trans. Autom. Control"},{"key":"27_CR32","doi-asserted-by":"crossref","unstructured":"Zhang, W., Chen, B.S.: General D-stability and D-stabilization for linear stochastic systems: contunuous-time case. The 8th IEEE International Conference on Control and Automation, June 9\u201311, Xiamen, China, 131\u2013136 (2010)","DOI":"10.1109\/ICCA.2010.5524067"},{"key":"27_CR33","unstructured":"Zhang, W., Chen, B.S.: $${\\cal H}$$ -representation and applications to generalized Lyapunov equations and linear stochastic systems. IEEE Trans. Autom. Control. 57(12), 3009\u20133022 (2012)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-0027-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-012-0027-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-0027-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T15:48:12Z","timestamp":1745941692000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-012-0027-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,4]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["27"],"URL":"https:\/\/doi.org\/10.1007\/s10898-012-0027-9","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2013,1,4]]}}}