Robust identification from band-limited data

Baratchart, Laurent; Leblond, Juliette; Partington, Jonathan R.; Torkhani, N.

doi:10.1109/9.623101

Cited by 26 publications

(19 citation statements)

References 16 publications

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“…Depending on the numerator/denominator orders of the model the amplitude of the transfer function can go to infinity outside the desired frequency band [6]. …”

Section: Increasing the Ordermentioning

confidence: 99%

Stable Approximations of Unstable Models

Dhaene

Pintelon

Guillaume

2007

2007 IEEE Instrumentation &Amp; Measurement Technology Conference IMTC 2007

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This paper considers the following problem: starting from noisy data a model for the transfer function is estimated. For afinite number of data points, the model is not guaranteed to be stable, even when the true linear system is known to be stable.[3] describes an iterative procedure for calculating a stable approximation of an unstable model. This paper presents an improved algorithm resulting in significantly smaller approximation errors. In addition stable minimax solutions can also be generated.

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“…Depending on the numerator/denominator orders of the model the amplitude of the transfer function can go to infinity outside the desired frequency band [6]. …”

Section: Increasing the Ordermentioning

confidence: 99%

Stable Approximations of Unstable Models

Dhaene

Pintelon

Guillaume

2007

2007 IEEE Instrumentation &Amp; Measurement Technology Conference IMTC 2007

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“…Other generalizations of the Nehari problem that have special cases in common with (H − OPT p ) have been considered. For example, if p = ∞, g is constant on ∂D \ K and g is so large on K that the constraint | f | ≤ g is not active on K , then (H − OPT p ) is a special case of a problem that has been studied by Baratchart, Leblond et al in the context of system identification ( [2]; see also [1,3]). Another related problem arising in H ∞ control theory has been studied by Helton et al (see, e.g., [6][7][8]10] and the references therein): Given a performance function Γ : ∂D × C → [0, ∞) one is interested in minimizing Γ (·, f (·)) L ∞ (∂D) over f ∈ H ∞ (D).…”

Section: Introductionmentioning

confidence: 98%

Constrained Hardy space approximation

Schneck

2010

Journal of Approximation Theory

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We consider the problem of minimizing the distance f − φ L p (K ) , where K is a subset of the complex unit circle ∂D and φ ∈ C(K ), subject to the constraint that f lies in the Hardy space H p (D) and | f | ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extremal property similar to that for the Nehari problem. Moreover, we prove that the minimum of the optimization problem can be approximated by smooth functions. This makes the problem accessible for numerical solution, with which we deal in a follow-up paper.

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“…The Nehari problem is very important in applications in control theory (see [6,13]) and is also a useful tool in identification, see [12,4]. Moreover, for the needs of control theory it is important to consider not only the scalar case, but also the case of matrix-valued functions.…”

Section: Introductionmentioning

confidence: 99%

Analytic approximation of matrix functions in Lp

Baratchart

Nazarov

Peller

2009

Journal of Approximation Theory

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We consider the problem of approximation of matrix functions of class L p on the unit circle by matrix functions analytic in the unit disk in the norm of L p , 2 ≤ p < ∞. For an m ×n matrix function Φ in L p , we consider the Hankel operator H Φ : H q (C n ) → H 2 − (C m ), 1/ p + 1/q = 1/2. It turns out that the space of m ×n matrix functions in L p splits into two subclasses: the set of respectable matrix functions and the set of weird matrix functions. If Φ is respectable, then its distance to the set of analytic matrix functions is equal to the norm of H Φ . For weird matrix functions, to obtain the distance formula, we consider Hankel operators defined on spaces of matrix functions. We also describe the set of p-badly approximable matrix functions in terms of special factorizations and give a parametrization formula for all best analytic approximants in the norm of L p . Finally, we introduce the notion of p-superoptimal approximation and prove the uniqueness of a p-superoptimal approximant for rational matrix functions.

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Robust identification from band-limited data

Cited by 26 publications

References 16 publications

Stable Approximations of Unstable Models

Stable Approximations of Unstable Models

Constrained Hardy space approximation

Analytic approximation of matrix functions in Lp

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