## Abstract

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 language | English (US) |
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Pages (from-to) | 1787-1791 |

Number of pages | 5 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

State | Published - Dec 1 1988 |

Event | Proceedings of the 27th IEEE Conference on Decision and Control - Austin, TX, USA Duration: Dec 7 1988 → Dec 9 1988 |

## ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization