Pole-zero identification based on simultaneous realization of normalized covariances and Markov parameters

Enqvist, Per

doi:10.1109/cdc.2002.1185035

Cited by 4 publications

(6 citation statements)

References 14 publications

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“…First the Markov and Covariance interpolation problem as formulated in [4] is described and then input-to-state filters are introduced for treating the generalized problem.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The states are then the n most recent outputs and it is easy to see that the covariance of the state is a Toeplitz matrix as in (4).…”

Section: B Input-to-state Filters and Interpolationmentioning

confidence: 99%

“…We could for example consider matching the constraints W (p 1 ) = q 1 , · · · , W (p n ) = q n for some points p 1 , · · · , p n in the unit disc and similarly for W W ⋆ . Most results in [4] carry over to this more general problem. A formal definition of the problem considered is given in the next section.…”

Section: Introductionmentioning

confidence: 99%

“…. , R q−1 a q-Markov COVariance Equivalent Realization (q-Markov COVER) and they have shown that if the data satisfies a particular consistency condition (which can be avoided using a variable input variance as in [4]), there are many such q-Markov COVERs and they are parameterized by a set of unitary matrices. One of the parameters considered "as known" in the classical q-Markov COVER theory is the variance of the input noise.…”

Section: Introductionmentioning

confidence: 99%

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Generalizing the Markov and covariance interpolation problem using input-to-state filters

Enqvist

2007

2007 European Control Conference (ECC)

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In the Markov and covariance interpolation problem a transfer function W is sought that match the first coefficients in the expansion of W around zero and the first coefficients of the Laurent expansion of the corresponding spectral density W W ⋆ . Here we solve an interpolation problem where the matched parameters are the coefficients of expansions of W and W W ⋆ around various points in the disc. The solution is derived using input-to-state filters and is determined by simple calculations such as solving Lyapunov equations and generalized eigenvalue problems.

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“…First the Markov and Covariance interpolation problem as formulated in [4] is described and then input-to-state filters are introduced for treating the generalized problem.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The states are then the n most recent outputs and it is easy to see that the covariance of the state is a Toeplitz matrix as in (4).…”

Section: B Input-to-state Filters and Interpolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalizing the Markov and covariance interpolation problem using input-to-state filters

Enqvist

2007

2007 European Control Conference (ECC)

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show abstract

“…The QMC theory was originally developed for model reduction Yousuff et al (1985), while the realization of all QMC from the input/output data of an unknown system is useful for identification Skelton and Shi (1996) Enqvist (2002). Unlike identification methods based on least squares, the q-Markov COVER gives a linear model that matches exactly the first q Markov parameters and the first q output covariance parameters Yousuff et al (1985)Liu and Skelton and Shi (1996).…”

Section: Introductionmentioning

confidence: 99%