Brief paper: Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

Authors:
P. Rapisarda;H. L. Trentelman
Affiliations:
ISIS Group, School of Electronics and Computer Science, University of Southampton, United Kingdom;Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

We illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.