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On estimation of the gain of a dynamical system
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0002-1927-1690
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-9368-3079
Uppsala University.
2011 (English)In: 2011 Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2011, IEEE , 2011, 364-369 p.Conference paper, Published paper (Refereed)
Abstract [en]

We analyze and compare methods to estimate the 2-gain ( ∞-norm) of a stable linear dynamical system, that is the maximum of the absolute value of the corresponding frequency response. The standard approach is to estimate a parametric model of the system, which then is used for gain calculation. An asymptotic error variance expression for ∞-norm estimates based on finite impulse response (FIR) models is presented. We then study the problem of finding the minimum variance excitation signal that satisfies a given error variance bound for the FIR model gain estimate. It is shown that a sinusoidal signal with frequency equal to the peak frequency of the system is minimum variance optimal. The second approach to gain estimation is based on iterative experiments, and is inspired by numerical methods eigenvalue calculation. The asymptotic statistical properties of such gain estimation methods are compared to the FIR model approach. A transparent expression for the additional variance cost of using iterative experiments is derived. Finally, we present some ideas for input sequence estimation based on iterative experiments.

Place, publisher, year, edition, pages
IEEE , 2011. 364-369 p.
Keyword [en]
Absolute values, Eigen-value, Error variance, Excitation signals, Finite-impulse response, FIR model, Gain estimation, Input sequence, Linear dynamical systems, Minimum variance, Norm estimates, Parametric models, Peak frequencies, Sinusoidal signals, Statistical properties, Digital signal processing, Dynamical systems, Eigenvalues and eigenfunctions, Experiments, FIR filters, Frequency response, Impulse response, Linear control systems, Numerical methods, Optimization, Signal processing, Estimation
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-55385DOI: 10.1109/DSP-SPE.2011.5739241ISI: 000298803400065Scopus ID: 2-s2.0-79954452883ISBN: 9781612842271 (print)OAI: oai:DiVA.org:kth-55385DiVA: diva2:471656
Conference
2011 Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2011. Sedona, AZ. 4 January 2011 - 7 January 2011
Note
© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20120104. Sponsors: Inst. Electr. Electron. Eng. (IEEE) Signal Process. Soc.Available from: 2012-01-31 Created: 2012-01-02 Last updated: 2013-09-05Bibliographically approved

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