Error bounds in the averaging of hybrid systems

J. Ezzine*, A. H. Haddad

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

6 Scopus citations


An analysis is made of the errors introduced by the averaging of hybrid systems. These 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 Baker-Campbell-Hausdorff (BCH) formula) provides a single system matrix as an approximation to the hybrid system. The two errors discussed are: (a) the error induced by the truncation of the BCH series expansion, and (b) 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)1787-1791
Number of pages5
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - Dec 1 1988
EventProceedings of the 27th IEEE Conference on Decision and Control - Austin, TX, USA
Duration: Dec 7 1988Dec 9 1988

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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