Title :
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
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;
Conference_Titel :
Decision and Control, 1988., Proceedings of the 27th IEEE Conference on
Conference_Location :
Austin, TX
DOI :
10.1109/CDC.1988.194635
