Error-bounds for balanced model-reduction of linear time-varying systems

Sanjay Lall, Carolyn Beck

Research output: Contribution to journalArticlepeer-review


Error-bounds are developed for balanced truncation of linear time-varying systems, leading to an extension of the "twice the sum of the tail" formulas, well known in the time-invariant case. The approach relies on an operator-theoretic framework for analysis of linear time-varying systems. This provides a multivariable notion of frequency for such systems, which are thus characterized by rational functions of many complex variables, allowing the problem to be formulated in the linear-fractional framework. Using a time-varying version of standard necessary conditions for reduced-order modeling, based on convex operator inequalities, we show that these error-bounds for balanced truncation are related to the closest possible reduced-order modeling error in a sense which parallels the time-invariant case.

Original languageEnglish (US)
Pages (from-to)946-956
Number of pages11
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 2003


  • Balanced truncation
  • Model reduction
  • Time-varying systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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