Error bounds in the averaging of hybrid systems

Author

Ezzine, J. ; Haddad, A.H.

Author_Institution

Sch. of Electr. Eng., Georgia Inst. of Technol., Atlanta, GA, USA

Volume

34

Issue

11

fYear

1989

fDate

11/1/1989 12:00:00 AM

Firstpage

1188

Lastpage

1192

Abstract

The authors analyze the error 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 instead of averaging to arrive at a time-invariant system matrix

Keywords

error analysis; feedback; linear systems; matrix algebra; time-varying systems; BCH series expansion; Backer-Campbell-Hausdorff; error bound analysis; finite state process; hybrid systems; linear systems; stability test; state feedback; system matrix; time varying systems; Control systems; H infinity control; Level set; Linear systems; Nonlinear control systems; Nonlinear systems; Output feedback; Sliding mode control; Switches; Time varying systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.40750

Filename

40750