Analytic Properties of Schmidt Pairs for a Hankel Operator and the Generalized Schur-Takagi Problem

Adamjan, Vadim; Arov, Damir Z.; Крейн, M. Г.

doi:10.1070/sm1971v015n01abeh001531

Cited by 598 publications

(364 citation statements)

References 9 publications

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“…The first decisive results in this direction were obtained by Adamjan, Arov, and Krein [1,2]. The theory as it is used today is due to Glover [36].…”

Section: Approximation Methodsmentioning

confidence: 95%

“…Consider the nonlinear system given by (1). For a fixed input ) , the state trajectory at certain instances of time % W is measured:…”

Section: Proper Orthogonal Decomposition (Pod) Methodsmentioning

confidence: 99%

“…We will briefly outline the construction method next. For details we refer to [1,2,36]; see also [8,9] as well as the books [13,62].…”

Section: Hankel Norm Approximationmentioning

confidence: 99%

See 2 more Smart Citations

Approximation of Large-Scale Dynamical Systems: An Overview

Antoulas

2004

IFAC Proceedings Volumes

147

179

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In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish among three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two.

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“…The first decisive results in this direction were obtained by Adamjan, Arov, and Krein [1,2]. The theory as it is used today is due to Glover [36].…”

Section: Approximation Methodsmentioning

confidence: 95%

“…Consider the nonlinear system given by (1). For a fixed input ) , the state trajectory at certain instances of time % W is measured:…”

Section: Proper Orthogonal Decomposition (Pod) Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Approximation of Large-Scale Dynamical Systems: An Overview

Antoulas

2004

IFAC Proceedings Volumes

147

179

View full text Add to dashboard Cite

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“…Interpolation has been considered in the class of meromorphic functions in S κ : Schur-Takagi problem [1], Nevanlinna-Pick problem [17], [13], [8]. However, not all functions in S κ are meromorphic.…”

Section: 1)mentioning

confidence: 99%

Nevanlinna–Pick interpolation: Pick matrices have bounded number of negative eigenvalues

Bolotnikov

Kheifets

Rodman

2003

Proc. Amer. Math. Soc.

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Abstract. The Nevanlinna-Pick interpolation problem is studied in the class of functions defined on the unit disk without a discrete set, with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. It is shown, in particular, that the degenerate problem always has a unique solution, not necessarily meromorphic. A related extension problem to a maximal function in the class is also studied.

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“…The approximation problem (15) can be solved using the famous AAK-lemma, see [17]. In particular, it is well-known that γ 1 (r)=σ r+1 (G) where σ i (G), i =1 ,...,n, are the Hankel singular values of the linear operator G, and methods for computing a state-space realization (A r ,K r ,C r ) of the optimal G * r are available, see [18], [19].…”

Section: Tha184mentioning

confidence: 99%

Reduced-order predictive outage compensators for networked systems

Henriksson

Johansson

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-Control systems utilizing wireless sensor and actuator networks can be severely affected by the properties of the wireless links. Radio fading and interference may cause communication outage of several samples in situations when the radio environment is noisy and low transmission power is desirable. We propose a method to compensate for outages by introducing a predictive outage compensator (POC), which is a filter to be implemented at the receiver sides of networked control systems and that generates artificial samples during the outage. The main contribution of the paper is to show that a POC can be derived based on a Kalman filter formulation and that it is possible to achieve good performance with a loworder implementation based on Hankel norm approximation. Tradeoffs between achievable closed-loop performance, outage length, and POC order are discussed. The results are illustrated on a simulated example of a multiple-tank process.

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Analytic Properties of Schmidt Pairs for a Hankel Operator and the Generalized Schur-Takagi Problem

Cited by 598 publications

References 9 publications

Approximation of Large-Scale Dynamical Systems: An Overview

Approximation of Large-Scale Dynamical Systems: An Overview

Nevanlinna–Pick interpolation: Pick matrices have bounded number of negative eigenvalues

Reduced-order predictive outage compensators for networked systems

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