Matrix pencils: Theory, applications, and numerical methods

Икрамов, Х. Д.

doi:10.1007/bf01098963

Cited by 31 publications

(14 citation statements)

References 45 publications

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“…Notice that (A + LC)E −1 S * ⊆ S * by the invariance property of S * [28], [49]. It follows that L and M are a pair of right deflating subspaces for the matrix pair (A + LC, E) [50], that is, M = AL + EL and dim(M) ≤ dim(L). The sparsity pattern in the descriptor and dynamic matricesẼ andÃ of (25) arises by construction of the right deflating subspaces P and Q [50, Eq.…”

Section: Centralized Attack Identificationmentioning

confidence: 99%

Attack Detection and Identification in Cyber-Physical Systems

Pasqualetti

Dörfler

Bullo

2013

IEEE Trans. Automat. Contr.

1,830

1,166

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Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial process control and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper (i) we propose a mathematical framework for cyberphysical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (iii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.

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Section: Centralized Attack Identificationmentioning

confidence: 99%

Attack Detection and Identification in Cyber-Physical Systems

Pasqualetti

Dörfler

Bullo

2013

IEEE Trans. Automat. Contr.

1,830

1,166

View full text Add to dashboard Cite

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“…We used a relatively modern approach to generating this model based on “matrix pencils” (Ikramov, 1993), or equivalently, the singular value decomposition (SVD) and total least squares (TLS) (Vanhuffel et al, 1994) of a Hankel matrix of the data. Although so-called “Prony analysis” has been studied for over a century (Kay and Marple, 1981; Marple, 1987), these more recent numerical methods have been successfully used to estimate or reconstruct unknown parameters of damped and undamped sinusoids in realistic noise (Hua and Sarkar, 1990), such as found in the free induction decay (FID) of nuclear magnetic resonance (Nieminen et al, 2010; Volegov et al, 2006).…”

Section: Methodsmentioning

confidence: 99%

The use of contact heat evoked potential stimulator (CHEPS) in magnetoencephalography for pain research

Gopalakrishnan

Machado

Burgess

2013

Journal of Neuroscience Methods

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Background Contact heat evoked potentials (CHEP) is a thermal stimulus modality used in pain research. We examine a commercial CHEP stimulator (CHEPS) that is designed to work in an fMRI environment, but poorly understood in the MEG environment. The CHEPS attains target temperatures rapidly using sophisticated control signals that unfortunately induce artifacts in the MEG. In this paper, we summarize our experiences using the CHEPS in MEG to study pain using an experimental paradigm, and propose a novel method for managing its artifact. New method We introduce a novel damped sinusoid modeling (DSM) technique to remove the CHEPS artifact based on estimates of the underlying sinusoids and damping factors. We show comparisons to signal space projection (SSP) and temporal signal space separation (tSSS) methods. Results The CHEPS artifact is highly dynamic, yet deterministic, switching rapidly from one frequency to another, with different spatial components. The galvanic connection between the subject and the CHEPS probe alters its performance, making pre-characterization difficult. Comparison with existing methods SSP methods failed to remove the artifact completely. TSSS performed better than SSP; however, tSSS requires the use of a multipolar head model that decreases the dimensionality and possibly the information content of the data. In contrast, DSM offers a strictly temporal modeling approach in which the artifact is estimated as a sum of damped sinusoids which is subtracted from the data. Conclusion Though the CHEPS increases the noise floor and introduces artifacts to the data, we believe the device can be successfully used in MEG if appropriate artifact removal techniques are followed.

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“…Matrix pencils arising in the theory of vibrations in the approximation of a time series with a sum of complex exponentials [5,7,8]. This paper surveys nearly all of the publications that have appeared in the last twenty years on the theory for random linear pencils.…”

Section: Introductionmentioning

confidence: 99%

“…x D E x without forming explicitly the matrix B 1 A (which could be impossible or ill-conditioned if B is singular or near-singular) [5,7,8]. Matrix pencils arising in the theory of vibrations in the approximation of a time series with a sum of complex exponentials [5,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…This paper surveys nearly all of the publications that have appeared in the last twenty years on the theory for random linear pencils. The survey is self-contained in the sense that it includes the necessary information from the elementary theory of random pencils and the theory of perturbations for the common random algebraic problem Ax D x ( [5,7,8] …”

Section: Introductionmentioning

confidence: 99%

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