Random matrix-based approach for uncertainty analysis of the eigensystem realization algorithm

Kumar Vishwajeet; Puneet Singla; Manoranjan Majji

doi:10.2514/1.G002469

Random matrix-based approach for uncertainty analysis of the eigensystem realization algorithm

Kumar Vishwajeet, Puneet Singla, Manoranjan Majji

Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, uncertainty in the state space matrices in a linear stochastic time-invariant discrete time system is presented by performing uncertainty analysis of the eigensystem realization algorithm (ERA). An analytical expression for the calculation of the singular values of Hankel matrix is developed. The expression for the joint distribution of the singular values is used to estimate the rank of the Hankel matrix. The distribution of singular values is also used to find the distribution on the bound of norm of system matrix.

Original language	English (US)
Pages (from-to)	1877-1891
Number of pages	15
Journal	Journal of Guidance, Control, and Dynamics
Volume	40
Issue number	8
DOIs	https://doi.org/10.2514/1.G002469
State	Published - 2017

All Science Journal Classification (ASJC) codes

Aerospace Engineering
Applied Mathematics
Electrical and Electronic Engineering
Control and Systems Engineering
Space and Planetary Science

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10.2514/1.G002469

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title = "Random matrix-based approach for uncertainty analysis of the eigensystem realization algorithm",

abstract = "In this paper, uncertainty in the state space matrices in a linear stochastic time-invariant discrete time system is presented by performing uncertainty analysis of the eigensystem realization algorithm (ERA). An analytical expression for the calculation of the singular values of Hankel matrix is developed. The expression for the joint distribution of the singular values is used to estimate the rank of the Hankel matrix. The distribution of singular values is also used to find the distribution on the bound of norm of system matrix.",

author = "Kumar Vishwajeet and Puneet Singla and Manoranjan Majji",

note = "Funding Information: This material is based upon the work jointly supported by the National Science Foundation under Award No. CMMI-1054759 and AFOSR Grants FA9550-11-1-0012 and FA9550-15-1-0313. Publisher Copyright: {\textcopyright} 2017 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.",

year = "2017",

doi = "10.2514/1.G002469",

language = "English (US)",

volume = "40",

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journal = "Journal of Guidance, Control, and Dynamics",

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publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",

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T1 - Random matrix-based approach for uncertainty analysis of the eigensystem realization algorithm

AU - Vishwajeet, Kumar

AU - Singla, Puneet

AU - Majji, Manoranjan

N1 - Funding Information: This material is based upon the work jointly supported by the National Science Foundation under Award No. CMMI-1054759 and AFOSR Grants FA9550-11-1-0012 and FA9550-15-1-0313. Publisher Copyright: © 2017 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

PY - 2017

Y1 - 2017

N2 - In this paper, uncertainty in the state space matrices in a linear stochastic time-invariant discrete time system is presented by performing uncertainty analysis of the eigensystem realization algorithm (ERA). An analytical expression for the calculation of the singular values of Hankel matrix is developed. The expression for the joint distribution of the singular values is used to estimate the rank of the Hankel matrix. The distribution of singular values is also used to find the distribution on the bound of norm of system matrix.

AB - In this paper, uncertainty in the state space matrices in a linear stochastic time-invariant discrete time system is presented by performing uncertainty analysis of the eigensystem realization algorithm (ERA). An analytical expression for the calculation of the singular values of Hankel matrix is developed. The expression for the joint distribution of the singular values is used to estimate the rank of the Hankel matrix. The distribution of singular values is also used to find the distribution on the bound of norm of system matrix.

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JF - Journal of Guidance, Control, and Dynamics

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ER -

Random matrix-based approach for uncertainty analysis of the eigensystem realization algorithm

Abstract

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