Balanced Model Reduction for Linear Time-Varying Symmetric Systems

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The goal of this paper is to develop balancing theory for the linear time-varying (LTV) symmetric systems. To this end, first we extend the concept of symmetry in terms of the dual system. Then, we define the cross Gramian for the LTV systems. For LTV symmetric systems, we establish a connection among the controllability, observability, and cross Gramians. In particular, if one of these three Gramians is obtained, the other two Gramians can be constructed. Based on this fact, we show that the symmetry structure is preserved under balanced truncation if the Hankel singular values are pointwise distinct.
Originele taal-2English
Pagina's (van-tot)3060-3067
Aantal pagina's8
TijdschriftIEEE Transactions on Automatic Control
Nummer van het tijdschrift7
StatusPublished - jul-2019

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