{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T19:21:35Z","timestamp":1778786495095,"version":"3.51.4"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2020,8]]},"DOI":"10.1007\/s10208-019-09426-y","type":"journal-article","created":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T20:07:52Z","timestamp":1565035672000},"page":"633-679","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":217,"title":["On the Sample Complexity of the Linear Quadratic Regulator"],"prefix":"10.1007","volume":"20","author":[{"given":"Sarah","family":"Dean","sequence":"first","affiliation":[]},{"given":"Horia","family":"Mania","sequence":"additional","affiliation":[]},{"given":"Nikolai","family":"Matni","sequence":"additional","affiliation":[]},{"given":"Benjamin","family":"Recht","sequence":"additional","affiliation":[]},{"given":"Stephen","family":"Tu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,5]]},"reference":[{"key":"9426_CR1","unstructured":"Y.\u00a0Abbasi-Yadkori and C.\u00a0Szepesv\u00e1ri. Regret Bounds for the Adaptive Control of Linear Quadratic Systems. In Proceedings of the 24th Annual Conference on Learning Theory, pages 1\u201326, 2011."},{"key":"9426_CR2","doi-asserted-by":"crossref","unstructured":"M.\u00a0Abeille and A.\u00a0Lazaric. Thompson sampling for linear-quadratic control problems. In AISTATS 2017-20th International Conference on Artificial Intelligence and Statistics, 2017.","DOI":"10.1214\/17-EJS1341SI"},{"key":"9426_CR3","unstructured":"M.\u00a0Abeille and A.\u00a0Lazaric. Improved regret bounds for thompson sampling in linear quadratic control problems. In International Conference on Machine Learning, pages 1\u20139, 2018."},{"key":"9426_CR4","doi-asserted-by":"crossref","unstructured":"J.\u00a0Anderson and N.\u00a0Matni. Structured state space realizations for sls distributed controllers. In 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 982\u2013987. IEEE, 2017.","DOI":"10.1109\/ALLERTON.2017.8262844"},{"key":"9426_CR5","unstructured":"M.\u00a0ApS. The MOSEK optimization toolbox for MATLAB manual. Version 8.1 (Revision 25)., 2015. URL http:\/\/docs.mosek.com\/8.1\/toolbox\/index.html ."},{"key":"9426_CR6","doi-asserted-by":"crossref","DOI":"10.1017\/9781139061759","volume-title":"Predictive control for linear and hybrid systems","author":"F Borrelli","year":"2017","unstructured":"F.\u00a0Borrelli, A.\u00a0Bemporad, and M.\u00a0Morari. Predictive control for linear and hybrid systems. Cambridge University Press, New York, NY, USA, 2017."},{"key":"9426_CR7","unstructured":"G.\u00a0E. Box, G.\u00a0M. Jenkins, G.\u00a0C. Reinsel, and G.\u00a0M. Ljung. Time series analysis: forecasting and control. John Wiley & Sons, 2015."},{"issue":"5","key":"9426_CR8","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1109\/9.284879","volume":"39","author":"RP Braatz","year":"1994","unstructured":"R.\u00a0P. Braatz, P.\u00a0M. Young, J.\u00a0C. Doyle, and M.\u00a0Morari. Computational complexity of $$\\mu $$ calculation. IEEE Transactions on Automatic Control, 39 (5): 1000\u20131002, 1994.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"9426_CR9","unstructured":"S.\u00a0J. Bradtke, B.\u00a0E. Ydstie, and A.\u00a0G. Barto. Adaptive linear quadratic control using policy iteration. In Proceedings of 1994 American Control Conference-ACC\u201994, volume\u00a03, pages 3475\u20133479. IEEE, 1994."},{"issue":"8","key":"9426_CR10","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1109\/TAC.2002.800750","volume":"47","author":"MC Campi","year":"2002","unstructured":"M.\u00a0C. Campi and E.\u00a0Weyer. Finite sample properties of system identification methods. IEEE Transactions on Automatic Control, 47 (8): 1329\u20131334, 2002.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"9426_CR11","unstructured":"J.\u00a0Chen and G.\u00a0Gu. Control-Oriented System Identification: An $$\\cal{H}_\\infty $$ Approach. Wiley, 2000."},{"key":"9426_CR12","unstructured":"J.\u00a0Chen and C.\u00a0N. Nett. The Caratheodory-Fejer problem and $$H_\\infty $$ identification: a time domain approach. In Proceedings of 32nd IEEE Conference on Decision and Control, pages 68\u201373. IEEE, 1993."},{"key":"9426_CR13","volume-title":"Control of uncertain systems: a linear programming approach","author":"MA Dahleh","year":"1994","unstructured":"M.\u00a0A. Dahleh and I.\u00a0J. Diaz-Bobillo. Control of uncertain systems: a linear programming approach. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1994."},{"key":"9426_CR14","unstructured":"S.\u00a0Dean, S.\u00a0Tu, N.\u00a0Matni, and B.\u00a0Recht. Safely Learning to Control the Constrained Linear Quadratic Regulator. arXiv:1809.10121, 2018."},{"key":"9426_CR15","doi-asserted-by":"publisher","unstructured":"J.\u00a0Doyle. Analysis of feedback systems with structured uncertainties. IEE Proceedings D - Control Theory and Applications, 129(6), 1982. ISSN 0143-7054. https:\/\/doi.org\/10.1049\/ip-d.1982.0053 .","DOI":"10.1049\/ip-d.1982.0053"},{"key":"9426_CR16","unstructured":"Y.\u00a0Duan, X.\u00a0Chen, R.\u00a0Houthooft, J.\u00a0Schulman, and P.\u00a0Abbeel. Benchmarking deep reinforcement learning for continuous control. In International Conference on Machine Learning, pages 1329\u20131338, 2016."},{"key":"9426_CR17","unstructured":"B.\u00a0Dumitrescu. Positive trigonometric polynomials and signal processing applications, volume 103. Springer Science & Business Media, 2007."},{"key":"9426_CR18","doi-asserted-by":"publisher","unstructured":"B.\u00a0Efron. Bootstrap Methods: Another Look at the Jackknife, pages 569\u2013593. Springer New York, New York, NY, 1992. https:\/\/doi.org\/10.1007\/978-1-4612-4380-9_41 .","DOI":"10.1007\/978-1-4612-4380-9_41"},{"key":"9426_CR19","doi-asserted-by":"publisher","unstructured":"M.\u00a0K.\u00a0H. Fan, A.\u00a0L. Tits, and J.\u00a0C. Doyle. Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Transactions on Automatic Control, 36(1), 1991. ISSN 0018-9286. https:\/\/doi.org\/10.1109\/9.62265 .","DOI":"10.1109\/9.62265"},{"key":"9426_CR20","unstructured":"M.\u00a0Fazel, R.\u00a0Ge, S.\u00a0Kakade, and M.\u00a0Mesbahi. Global convergence of policy gradient methods for the linear quadratic regulator. In Proceedings of the 35th International Conference on Machine Learning, volume\u00a080, pages 1467\u20131476. PMLR, 10\u201315 Jul 2018."},{"issue":"1","key":"9426_CR21","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1137\/S0363012994266504","volume":"35","author":"E Feron","year":"1997","unstructured":"E.\u00a0Feron. Analysis of robust $${\\cal{H}}_2$$ performance using multiplier theory. SIAM Journal on Control and Optimization, 35 (1): 160\u2013177, 1997. 10.1137\/S0363012994266504.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"9426_CR22","doi-asserted-by":"publisher","unstructured":"C.-N. Fiechter. PAC adaptive control of linear systems. In Proceedings of the Tenth Annual Conference on Computational Learning Theory, COLT \u201997, pages 72\u201380, New York, NY, USA, 1997. ACM. https:\/\/doi.org\/10.1145\/267460.267481 .","DOI":"10.1145\/267460.267481"},{"issue":"2","key":"9426_CR23","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/18.661510","volume":"44","author":"A Goldenshluger","year":"1998","unstructured":"A.\u00a0Goldenshluger. Nonparametric estimation of transfer functions: rates of convergence and adaptation. IEEE Transactions on Information Theory, 44 (2): 644\u2013658, 1998. https:\/\/doi.org\/10.1109\/18.661510 .","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"9426_CR24","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1214\/aos\/1009210547","volume":"29","author":"A Goldenshluger","year":"2001","unstructured":"A.\u00a0Goldenshluger and A.\u00a0Zeevi. Nonasymptotic bounds for autoregressive time series modeling. Ann. Statist., 29 (2): 417\u2013444, 04 2001. 10.1214\/aos\/1009210547.","journal-title":"Ann. Statist."},{"key":"9426_CR25","unstructured":"P.\u00a0Hall. The Bootstrap and Edgeworth Expansion. Springer Science & Business Media, 2013."},{"issue":"1","key":"9426_CR26","first-page":"1025","volume":"19","author":"M Hardt","year":"2018","unstructured":"M.\u00a0Hardt, T.\u00a0Ma, and B.\u00a0Recht. Gradient descent learns linear dynamical systems. The Journal of Machine Learning Research, 19 (1): 1025\u20131068, 2018.","journal-title":"The Journal of Machine Learning Research"},{"key":"9426_CR27","unstructured":"E.\u00a0Hazan, K.\u00a0Singh, and C.\u00a0Zhang. Learning linear dynamical systems via spectral filtering. In Advances in Neural Information Processing Systems, pages 6702\u20136712, 2017."},{"key":"9426_CR28","unstructured":"E.\u00a0Hazan, H.\u00a0Lee, K.\u00a0Singh, C.\u00a0Zhang, and Y.\u00a0Zhang. Spectral filtering for general linear dynamical systems. In Advances in Neural Information Processing Systems, pages 4634\u20134643, 2018."},{"issue":"10","key":"9426_CR29","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1109\/9.90229","volume":"36","author":"A.\u00a0J Helmicki","year":"1991","unstructured":"A.\u00a0J. Helmicki, C.\u00a0A. Jacobson, and C.\u00a0N. Nett. Control oriented system identification: a worst-case\/deterministic approach in $$\\cal{H}_\\infty $$. IEEE Transactions on Automatic Control, 36 (10): 1163\u20131176, 1991. 10.1109\/9.90229.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"9426_CR30","unstructured":"M.\u00a0Ibrahimi, A.\u00a0Javanmard, and B.\u00a0V. Roy. Efficient reinforcement learning for high dimensional linear quadratic systems. In F.\u00a0Pereira, C.\u00a0J.\u00a0C. Burges, L.\u00a0Bottou, and K.\u00a0Q. Weinberger, editors, Advances in Neural Information Processing Systems 25, pages 2636\u20132644, 2012."},{"key":"9426_CR31","unstructured":"N.\u00a0Jiang, A.\u00a0Krishnamurthy, A.\u00a0Agarwal, J.\u00a0Langford, and R.\u00a0E. Schapire. Contextual decision processes with low Bellman rank are PAC-learnable. In Proceedings of the 34th International Conference on Machine Learning, volume\u00a070, pages 1704\u20131713. PMLR, 06\u201311 Aug 2017."},{"key":"9426_CR32","doi-asserted-by":"crossref","unstructured":"E.\u00a0Jonas, Q.\u00a0Pu, S.\u00a0Venkataraman, I.\u00a0Stoica, and B.\u00a0Recht. Occupy the cloud: Distributed computing for the 99%. In Proceedings of the 2017 Symposium on Cloud Computing, pages 445\u2013451. ACM, 2017. 10.1145\/3127479.3128601.","DOI":"10.1145\/3127479.3128601"},{"issue":"1","key":"9426_CR33","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s10994-016-5588-2","volume":"106","author":"V Kuznetsov","year":"2017","unstructured":"V.\u00a0Kuznetsov and M.\u00a0Mohri. Generalization bounds for non-stationary mixing processes. Machine Learning, 106 (1): 93\u2013117, 2017. https:\/\/doi.org\/10.1007\/s10994-016-5588-2 .","journal-title":"Machine Learning"},{"issue":"1","key":"9426_CR34","first-page":"1334","volume":"17","author":"S Levine","year":"2016","unstructured":"S.\u00a0Levine, C.\u00a0Finn, T.\u00a0Darrell, and P.\u00a0Abbeel. End-to-end training of deep visuomotor policies. Journal of Machine Learning Research, 17 (1): 1334\u20131373, Jan. 2016.","journal-title":"Journal of Machine Learning Research"},{"key":"9426_CR35","unstructured":"W.\u00a0Li and E.\u00a0Todorov. Iterative Linear Quadratic Regulator Design for Nonlinear Biological Movement Systems. In International Conference on Informatics in Control, Automation and Robotics, 2004."},{"key":"9426_CR36","volume-title":"System Identification: Theory for the User","author":"L Ljung","year":"1999","unstructured":"L.\u00a0Ljung. System Identification: Theory for the User. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1999."},{"key":"9426_CR37","unstructured":"J.\u00a0L\u00f6fberg. YALMIP : A toolbox for modeling and optimization in MATLAB. In IEEE International Symposium on Computer Aided Control System Design, 2004."},{"key":"9426_CR38","doi-asserted-by":"publisher","unstructured":"N.\u00a0Matni, Y.\u00a0Wang, and J.\u00a0Anderson. Scalable system level synthesis for virtually localizable systems. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pages 3473\u20133480, Dec 2017. https:\/\/doi.org\/10.1109\/CDC.2017.8264168 .","DOI":"10.1109\/CDC.2017.8264168"},{"issue":"1","key":"9426_CR39","first-page":"1044","volume":"18","author":"DJ McDonald","year":"2017","unstructured":"D.\u00a0J. McDonald, C.\u00a0R. Shalizi, and M.\u00a0Schervish. Nonparametric risk bounds for time-series forecasting. Journal of Machine Learning Research, 18 (1): 1044\u20131083, Jan. 2017.","journal-title":"Journal of Machine Learning Research"},{"issue":"6","key":"9426_CR40","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1109\/9.587335","volume":"42","author":"A Megretski","year":"1997","unstructured":"A.\u00a0Megretski and A.\u00a0Rantzer. System analysis via integral quadratic constraints. IEEE Transactions on Automatic Control, 42(6): 819\u2013830, June 1997. https:\/\/doi.org\/10.1109\/9.587335 .","journal-title":"IEEE Transactions on Automatic Control"},{"key":"9426_CR41","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1038\/nature14236","volume":"518","author":"V Mnih","year":"2015","unstructured":"V.\u00a0Mnih, K.\u00a0Kavukcuoglu, D.\u00a0Silver, A.\u00a0A. Rusu, J.\u00a0Veness, M.\u00a0G. Bellemare, A.\u00a0Graves, M.\u00a0Riedmiller, A.\u00a0K. Fidjeland, G.\u00a0Ostrovski, S.\u00a0Petersen, C.\u00a0Beattie, A.\u00a0Sadik, I.\u00a0Antonoglou, H.\u00a0King, D.\u00a0Kumaran, D.\u00a0Wierstra, S.\u00a0Legg, and D.\u00a0Hassabis. Human-level control through deep reinforcement learning. Nature, 518: 529\u2013533, 02 2015.","journal-title":"Nature"},{"key":"9426_CR42","first-page":"789","volume":"11","author":"M Mohri","year":"2010","unstructured":"M.\u00a0Mohri and A.\u00a0Rostamizadeh. Stability bounds for stationary $$\\phi $$-mixing and $$\\beta $$-mixing processes. Journal of Machine Learning Research, 11: 789\u2013814, 2010.","journal-title":"Journal of Machine Learning Research"},{"key":"9426_CR43","doi-asserted-by":"publisher","unstructured":"Y.\u00a0Ouyang, M.\u00a0Gagrani, and R.\u00a0Jain. Control of unknown linear systems with thompson sampling. In 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1198\u20131205, Oct 2017. https:\/\/doi.org\/10.1109\/ALLERTON.2017.8262873 .","DOI":"10.1109\/ALLERTON.2017.8262873"},{"issue":"1","key":"9426_CR44","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0005-1098(93)90175-S","volume":"29","author":"A Packard","year":"1993","unstructured":"A.\u00a0Packard and J.\u00a0Doyle. The complex structured singular value. Automatica, 29 (1): 71 \u2013 109, 1993. https:\/\/doi.org\/10.1016\/0005-1098(93)90175-S .","journal-title":"Automatica"},{"key":"9426_CR45","doi-asserted-by":"publisher","unstructured":"F.\u00a0Paganini. Necessary and sufficient conditions for robust $${\\cal{H}}_2$$ performance. In Proceedings of 1995 34th IEEE Conference on Decision and Control, volume\u00a02, pages 1970\u20131975 vol.2, Dec 1995. https:\/\/doi.org\/10.1109\/CDC.1995.480635 .","DOI":"10.1109\/CDC.1995.480635"},{"key":"9426_CR46","unstructured":"J.\u00a0Pereira, M.\u00a0Ibrahimi, and A.\u00a0Montanari. Learning networks of stochastic differential equations. In Advances in Neural Information Processing Systems, pages 172\u2013180, 2010."},{"issue":"6","key":"9426_CR47","doi-asserted-by":"publisher","first-page":"2736","DOI":"10.1109\/TAC.2016.2616644","volume":"62","author":"R Postoyan","year":"2017","unstructured":"R.\u00a0Postoyan, L.\u00a0Bu\u015foniu, D.\u00a0Ne\u0161i\u0107, and J.\u00a0Daafouz. Stability analysis of discrete-time infinite-horizon optimal control with discounted cost. IEEE Transactions on Automatic Control, 62 (6): 2736\u20132749, June 2017. https:\/\/doi.org\/10.1109\/TAC.2016.2616644 .","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"6","key":"9426_CR48","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1016\/0005-1098(95)00024-Q","volume":"31","author":"L Qiu","year":"1995","unstructured":"L.\u00a0Qiu, B.\u00a0Bernhardsson, A.\u00a0Rantzer, E.\u00a0Davison, P.\u00a0Young, and J.\u00a0Doyle. A formula for computation of the real stability radius. Automatica, 31 (6): 879 \u2013 890, 1995. https:\/\/doi.org\/10.1016\/0005-1098(95)00024-Q .","journal-title":"Automatica"},{"issue":"1","key":"9426_CR49","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000070","volume":"11","author":"DJ Russo","year":"2018","unstructured":"D.\u00a0J. Russo, B.\u00a0Van\u00a0Roy, A.\u00a0Kazerouni, I.\u00a0Osband, and Z.\u00a0Wen. A tutorial on thompson sampling. Foundations and Trends on Machine Learning, 11(1): 1\u201396, 2018. https:\/\/doi.org\/10.1561\/2200000070 .","journal-title":"Foundations and Trends on Machine Learning"},{"key":"9426_CR50","unstructured":"J.\u00a0Shao and D.\u00a0Tu. The Jackknife and Bootstrap. Springer Science & Business Media, 2012."},{"key":"9426_CR51","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1038\/nature16961","volume":"529","author":"D Silver","year":"2016","unstructured":"D.\u00a0Silver, A.\u00a0Huang, C.\u00a0J. Maddison, A.\u00a0Guez, L.\u00a0Sifre, G.\u00a0van\u00a0den Driessche, J.\u00a0Schrittwieser, I.\u00a0Antonoglou, V.\u00a0Panneershelvam, M.\u00a0Lanctot, S.\u00a0Dieleman, D.\u00a0Grewe, J.\u00a0Nham, N.\u00a0Kalchbrenner, I.\u00a0Sutskever, T.\u00a0Lillicrap, M.\u00a0Leach, K.\u00a0Kavukcuoglu, T.\u00a0Graepel, and D.\u00a0Hassabis. Mastering the game of go with deep neural networks and tree search. Nature, 529: 484\u2013489, 01 2016.","journal-title":"Nature"},{"key":"9426_CR52","unstructured":"M.\u00a0Simchowitz, H.\u00a0Mania, S.\u00a0Tu, M.\u00a0I. Jordan, and B.\u00a0Recht. Learning without mixing: Towards a sharp analysis of linear system identification. In Proceedings of the 31st Conference On Learning Theory, volume\u00a075, pages 439\u2013473. PMLR, 06\u201309 Jul 2018."},{"issue":"6","key":"9426_CR53","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1016\/S0005-1098(01)00299-0","volume":"38","author":"M Sznaier","year":"2002","unstructured":"M.\u00a0Sznaier, T.\u00a0Amishima, P.\u00a0Parrilo, and J.\u00a0Tierno. A convex approach to robust $${\\cal{H}}_2$$ performance analysis. Automatica, 38 (6): 957 \u2013 966, 2002. https:\/\/doi.org\/10.1016\/S0005-1098(01)00299-0 .","journal-title":"Automatica"},{"key":"9426_CR54","unstructured":"S.\u00a0Tu, R.\u00a0Boczar, A.\u00a0Packard, and B.\u00a0Recht. Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification. arXiv:1707.04791, 2017."},{"key":"9426_CR55","doi-asserted-by":"crossref","unstructured":"A.\u00a0W. Van Der\u00a0Vaart and J.\u00a0A. Wellner. Weak Convergence and Empirical Processes. Springer Science & Business Media, 1996.","DOI":"10.1007\/978-1-4757-2545-2_3"},{"key":"9426_CR56","unstructured":"R.\u00a0Vershynin. Introduction to the non-asymptotic analysis of random matrices. arXiv:1011.3027, 2010."},{"issue":"3","key":"9426_CR57","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1016\/j.jprocont.2007.10.009","volume":"18","author":"M Vidyasagar","year":"2008","unstructured":"M.\u00a0Vidyasagar and R.\u00a0L. Karandikar. A learning theory approach to system identification and stochastic adaptive control. Journal of Process Control, 18 (3): 421 \u2013 430, 2008. https:\/\/doi.org\/10.1016\/j.jprocont.2007.10.009 .","journal-title":"Journal of Process Control"},{"key":"9426_CR58","doi-asserted-by":"publisher","unstructured":"M.\u00a0J. Wainwright. High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 2019. https:\/\/doi.org\/10.1017\/9781108627771 .","DOI":"10.1017\/9781108627771"},{"key":"9426_CR59","doi-asserted-by":"publisher","unstructured":"Y.\u00a0Wang, N.\u00a0Matni, and J.\u00a0C. Doyle. A system level approach to controller synthesis. IEEE Transactions on Automatic Control, pages 1\u20131, 2019. https:\/\/doi.org\/10.1109\/TAC.2018.2890753 .","DOI":"10.1109\/TAC.2018.2890753"},{"key":"9426_CR60","doi-asserted-by":"publisher","unstructured":"F.\u00a0Wu and A.\u00a0Packard. Optimal lqg performance of linear uncertain systems using state-feedback. In Proceedings of 1995 American Control Conference - ACC\u201995, volume\u00a06, pages 4435\u20134439, June 1995. https:\/\/doi.org\/10.1109\/ACC.1995.532775 .","DOI":"10.1109\/ACC.1995.532775"},{"issue":"3","key":"9426_CR61","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1109\/TAC.1976.1101223","volume":"21","author":"D Youla","year":"1976","unstructured":"D.\u00a0Youla, H.\u00a0Jabr, and J.\u00a0Bongiorno. Modern wiener-hopf design of optimal controllers\u2013part ii: The multivariable case. IEEE Transactions on Automatic Control, 21 (3): 319\u2013338, 1976. https:\/\/doi.org\/10.1109\/TAC.1976.1101223 .","journal-title":"IEEE Transactions on Automatic Control"},{"key":"9426_CR62","doi-asserted-by":"publisher","unstructured":"P.\u00a0M. Young, M.\u00a0P. Newlin, and J.\u00a0C. Doyle. $$\\mu $$ analysis with real parametric uncertainty. In Proceedings of the 30th IEEE Conference on Decision and Control, volume\u00a02, pages 1251\u20131256, Dec 1991. https:\/\/doi.org\/10.1109\/CDC.1991.261579 .","DOI":"10.1109\/CDC.1991.261579"},{"issue":"1","key":"9426_CR63","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1214\/aop\/1176988849","volume":"22","author":"B Yu","year":"1994","unstructured":"B.\u00a0Yu. Rates of convergence for empirical processes of stationary mixing sequences. The Annals of Probability, 22 (1): 94\u2013116, 1994.","journal-title":"The Annals of Probability"},{"key":"9426_CR64","volume-title":"Robust and Optimal Control","author":"K Zhou","year":"1996","unstructured":"K.\u00a0Zhou, J.\u00a0C. Doyle, and K.\u00a0Glover. Robust and Optimal Control. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1996."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-019-09426-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-019-09426-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-019-09426-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,25]],"date-time":"2022-09-25T05:40:45Z","timestamp":1664084445000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-019-09426-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,5]]},"references-count":64,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["9426"],"URL":"https:\/\/doi.org\/10.1007\/s10208-019-09426-y","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,5]]},"assertion":[{"value":"8 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 December 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 February 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}