Identification of stable models in subspace identification by using regularization
(2001) IEEE Transactions on Automatic Control — Vol. 46, n° 9, p. 1416-1420 (2001)
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- Abstract
- In subspace identification methods, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. Fora finite number of data points, the estimated system matrix is not guaranteed to be stable, even when the true linear system is known to be stable. In this note, stability is imposed by using regularization. The regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive (semi) definite weighting matrix. The amount of regularization can be determined from a generalized eigenvalue problem. The data augmentation method of Chui and Maciejowski is obtained by using specific choices for the weighting matrix in the regularization term.
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Van Gestel, T., Suykens, J., Van Dooren, P., & De Moor, B. (2001). Identification of stable models in subspace identification by using regularization. IEEE Transactions on Automatic Control, 46(9), 1416-1420. https://doi.org/10.1109/9.948469 (Original work published 2001)