Singular decompositions of state-covariances

Tryphon T. Georgiou

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Singularities in second-order statistics reveal linear dependencies between correlation variables. This fact underlies techniques ranging from Gauss' least squares to modern subspace methods in system identification. In particular, the latter exploit a decomposition of covariance data according to a hypothesis that the stochastic process breaks up into a sum of a deterministic component plus white noise. In the present paper we continue our earlier studies [9], [10] on the correspondence between state-covariances and input power spectra in dynamical systems. We characterize state-covariances which correspond to deterministic inputs and develop formulae for the input spectrum of a singular state-covariance. We show that multivariable decomposition of a state-covariance in accordance with a "deterministic component + white noise" hypothesis for the input does not exist in general, and study a possible alternative where the "white noise" is replaced with a general "moving-average process" having "short-range correlation structure". The decomposition according to the range of their time-domain correlations is an alternative to the well-known (Carathéodory- Fejér-)Pisarenko decomposition of Toeplitz matrices with potentially great practical significance, and can be determined via convex optimization.

Original languageEnglish (US)
Title of host publicationProceedings of the 2006 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1424402107, 9781424402106
StatePublished - 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: Jun 14 2006Jun 16 2006

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2006 American Control Conference
Country/TerritoryUnited States
CityMinneapolis, MN


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