Balanced Model Reduction for Linear Time-Varying Symmetric Systems

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Abstract

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.
Original languageEnglish
Pages (from-to)3060-3067
Number of pages8
JournalIEEE Transactions on Automatic Control
Volume64
Issue number7
DOIs
Publication statusPublished - Jul-2019

Keywords

  • VARIABLE SYSTEMS
  • TRUNCATION
  • STABILITY

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