Abstract
The Loewner matrix framework can identify the underlying system from given noise-free measurements either in the frequency, or in the time domain[1, 2]. This paper provides an analysis of the effects of noise on the performance of the SVD implementation of the Loewner matrix framework for different noise levels and proposes an improved approach which is able to identify an approximation of the original system even for high levels of noise. Moreover, for frequency domain measurements, our framework can handle systems with a large number of inputs and outputs while requiring small computational time and storage.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lefteriu, S., Antoulas, A.C.: A new approach to modeling multi-port systems from frequency domain data. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 29(1), 14–27 (2010)
Mayo, A.J., Antoulas, A.C.: A framework for the solution of the generalized realization problem. Linear Algebra and its Applications 405, 634–662 (2007)
Gustavsen, B., Semlyen, A.: Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Del. 14, 1052–1061 (1999)
Yip, E., Sincovec, R.: Solvability, controllability, and observability of continuous descriptor systems. IEEE Trans. Autom. Control 26, 702–707 (1981)
Lefteriu, S., Antoulas, A.: Topics in model order reduction with applications to circuit simulation. In: Proc. Model Reduction for Circuit Simulation Workshop. Springer, Heidelberg (2009) (under review)
Peeters, B., der Auweraer, H.V., Guillaume, P., Leuridan, J.: The polymax frequency-domain method: a new standard for modal parameter estimation? Sound and Vibration 11, 395–409 (2004)
Wright, T.G.: EigTool (2002), http://www.comlab.ox.ac.uk/projects/pseudospectra/eigtool
Trefethen, L.N., Embree, M.: Spectra and Pseudospectra: the Behaviour of Nonnormal Matrices and Operators. SIAM, Philadelphia (2005)
Ho, B., Kalman, R.: Effective construction of linear, state-variable models from input/output function. Regelungstechnik 14, 545–548 (1966)
Silverman, L.: Realizations of linear dynamical systems. IEEE Trans. Autom. Control 16, 554–567 (1971)
Antoulas, A.C., Anderson, B.D.O.: On the scalar rational interpolation problem. IMA J. of Mathematical Control and Information 3, 61–88 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lefteriu, S., Ionita, A.C., Antoulas, A.C. (2010). Modeling Systems Based on Noisy Frequency and Time Domain Measurements. In: Willems, J.C., Hara, S., Ohta, Y., Fujioka, H. (eds) Perspectives in Mathematical System Theory, Control, and Signal Processing. Lecture Notes in Control and Information Sciences, vol 398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93918-4_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-93918-4_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-93917-7
Online ISBN: 978-3-540-93918-4
eBook Packages: EngineeringEngineering (R0)