Finite Sample Analysis of Stochastic System Identification

——, “Perturbation bounds in connection with singular value decomposition,” BIT Numerical Mathematics , vol. 12, no. 1, pp. 99–111, 1972

1972

Earlier work this paper cites.

P.-Å. Wedin, “Perturbation theory for pseudo-inverses,” BIT Numerical Mathematics , vol. 13, no. 2, pp. 217–232, 1973

1973

Earlier work this paper cites.

L. Pernebo and L. Silverman, “Model reduction via balanced state space representations,” IEEE Transactions on Automatic Control , vol. 27, no. 2, pp. 382–387, 1982

1982

Earlier work this paper cites.

——, Topics in Matrix Analysis . Cambridge University Press, 1994

1994

Earlier work this paper cites.

M. Deistler, K. Peternell, and W. Scherrer, “Consistency and relative efficiency of subspace methods,” Automatica , vol. 31, no. 12, pp. 1865–1875, 1995

1995

Earlier work this paper cites.

P. Van Overschee and B. De Moor, “A Unifying Theorem for Three Subspace System Identification Algorithms,” Automatica , vol. 31, no. 12, pp. 1853–1864, 1995

1995

Earlier work this paper cites.

K. Peternell, W. Scherrer, and M. Deistler, “Statistical analysis of novel subspace identification methods,” Signal Processing , vol. 52, no. 2, pp. 161–177, 1996

1996

Earlier work this paper cites.

M. Viberg, B. Wahlberg, and B. Ottersten, “Analysis of state space system identification methods based on instrumental variables and subspace fitting,” Automatica , vol. 33, no. 9, pp. 1603–1616, 1997

1997

Earlier work this paper cites.

M. Jansson and B. Wahlberg, “On consistency of subspace methods for system identification,” Automatica , vol. 34, no. 12, pp. 1507–1519, 1998

1998

Earlier work this paper cites.

L. Ljung, System Identification: Theory for the User . Prentice Hall, 1999

1999

Earlier work this paper cites.

D. Bauer, M. Deistler, and W. Scherrer, “Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs,” Automatica , vol. 35, no. 7, pp. 1243–1254, 1999

1999

Earlier work this paper cites.

E. Weyer, R. C. Williamson, and I. M. Mareels, “Finite sample properties of linear model identification,” IEEE Transactions on Automatic Control , vol. 44, no. 7, pp. 1370–1383, 1999

1999

Cited alongside, same era.

T. Knudsen, “Consistency analysis of subspace identification methods based on a linear regression approach,” Automatica , vol. 37, no. 1, pp. 81–89, 2001

2001

Cited alongside, same era.

M. C. Campi and E. Weyer, “Finite sample properties of system identification methods,” IEEE Transactions on Automatic Control , vol. 47, no. 8, pp. 1329–1334, 2002

2002

Cited alongside, same era.

B. Anderson and J. Moore, Optimal Filtering . Dover Publications, 2005

2005

Cited alongside, same era.

S. J. Qin, “An overview of subspace identification,” Computers & chemical engineering , vol. 30, no. 10-12, pp. 1502–1513, 2006

2006

F. Krahmer, S. Mendelson, and H. Rauhut, “Suprema of chaos processes and the restricted isometry property,” Communications on Pure and Applied Mathematics , vol. 67, no. 11, pp. 1877–1904, 2014

2014

Later among the works it cites.

S. Tu, R. Boczar, M. Simchowitz, M. Soltanolkotabi, and B. Recht, “Low-rank solutions of linear matrix equations via procrustes flow,” in International Conference on Machine Learning , 2016, pp. 964–973

2016

Later among the works it cites.

S. Dean, H. Mania, N. Matni, B. Recht, and S. Tu, “On the sample complexity of the linear quadratic regulator,” arXiv preprint arXiv:1710.01688 , 2017

Original

2017

Later among the works it cites.

M. K. S. Faradonbeh, A. Tewari, and G. Michailidis, “Finite time identification in unstable linear systems,” Automatica , vol. 96, pp. 342–353, 2018

2018

Later among the works it cites.