A Note on Spectral Conditions for Positive Realness of Transfer Function Matrices

Shorten, Robert; Curran, Paul; Wulff, Kai; Zeheb, E.

doi:10.1109/tac.2008.919553

Cited by 35 publications

(17 citation statements)

References 12 publications

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“…The literature contains spectral conditions for checking SPR of a strictly proper transfer function [10]; however, these conditions involve the eigenvalues of a 2n 2 2n Hamiltonian matrix. The conditions here involve a matrix of dimension n 2 n.…”

Section: ) Commentmentioning

confidence: 99%

Quadratic Stability and Singular SISO Switching Systems

Shorten

Corless

Wulff

et al. 2009

IEEE Trans. Automat. Contr.

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Abstract-In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form , , and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of the product ( ). The technical note also contains a spectral characterization of strictly positive real transfer functions which are strictly proper. Examples are presented to illustrate our results.Index Terms-LTI systems.

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Section: ) Commentmentioning

confidence: 99%

Quadratic Stability and Singular SISO Switching Systems

Shorten

Corless

Wulff

et al. 2009

IEEE Trans. Automat. Contr.

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“…To this end, consider the nonlinear system: . It is easily verified that the transfer function G(s) = w T (sI − A) −1 b is strictly positive real; see [23]. Since the positive orthant is selfdual, it follows from Theorem 2 that the differential equation given by Eq.…”

Section: Examplesmentioning

confidence: 88%

An extension of the KYP-lemma for the design of state-dependent switching systems with uncertainty

King

Shorten

2013

Systems & Control Letters

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“…Once Y r (s, g) is transformed into a standard state-space form, its passivity can be verified by computing the eigenvalues of an associated Hamiltonian matrix [49] singularity exists, the modified Hamiltonian-based passivity check proposed in [50] should be used.…”

Section: Passivity Assessment Considerationsmentioning

confidence: 99%

Physics-Based Passivity-Preserving Parameterized Model Order Reduction for PEEC Circuit Analysis

Ferranti

Antonini

Dhaene

et al. 2011

IEEE Trans. Compon., Packag. Manufact. Technol.

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Abstract-The decrease of integrated circuit feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods, and model order reduction (MOR) methods have proven to be very effective in combating such high complexity. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the circuit under study as a function of design parameters such as geometrical and substrate features. Traditional MOR techniques perform order reduction only with respect to frequency, and therefore the computation of a new electromagnetic model and the corresponding reduced model are needed each time a design parameter is modified, reducing the CPU efficiency. Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We propose a novel PMOR technique applicable to PEEC analysis which is based on a parameterization process of matrices generated by the PEEC method and the projection subspace generated by a passivity-preserving MOR method. The proposed PMOR technique guarantees overall stability and passivity of parameterized reduced order models over a user-defined range of design parameter values. Pertinent numerical examples validate the proposed PMOR approach.Index Terms-Interpolation, parameterized model order reduction, partial element equivalent circuit method, passivity.

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A Note on Spectral Conditions for Positive Realness of Transfer Function Matrices

Cited by 35 publications

References 12 publications

Quadratic Stability and Singular SISO Switching Systems

Quadratic Stability and Singular SISO Switching Systems

An extension of the KYP-lemma for the design of state-dependent switching systems with uncertainty

Physics-Based Passivity-Preserving Parameterized Model Order Reduction for PEEC Circuit Analysis

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