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.
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering