Error Bounds in the Averaging of Hybrid Systems

J. Ezzine, A. H. Haddad

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


This note analyzes the errors introduced by the averaging of hybrid systems. These systems involve linear systems which can take a number of different realizations based on the state of an underlying finite state process. The averaging technique (based on a formula from Lie algebras known as the Backer Campbell Hausdorff (BCH) formula) provides a single system matrix as an approximation to the hybrid system. The two errors discussed are: 1) the error induced by the truncation of the BCH series expansion; and 2) the error between the actual hybrid system and its average. A simple sufficient stability test is proposed to check the asymptotic behavior of this error. In addition, conditions are derived that allow the use of state feedback to arrive at a time-invariant system matrix instead of averaging.

Original languageEnglish (US)
Pages (from-to)1188-1192
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number11
StatePublished - Nov 1989

ASJC Scopus subject areas

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


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