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

fYear

1988

fDate

7-9 Dec 1988

Firstpage

1787

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

Keywords

algebra; linear systems; time-varying systems; Baker-Campbell-Hausdorff formula; Lie algebras; asymptotic behavior; averaging; error bounds; hybrid systems; linear systems; series expansion; sufficient stability test; time varying systems; time-invariant system matrix; Algebra; Asymptotic stability; Control systems; Equations; Error analysis; Linear systems; Nonlinear systems; State feedback; Switches; Testing;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1988., Proceedings of the 27th IEEE Conference on

Conference_Location

Austin, TX

Type

conf

DOI

10.1109/CDC.1988.194635

Filename

194635