DocumentCode :
1067966
Title :
Author :
Roberson, D. Gray ; Stilwell, Daniel J.
Author_Institution :
Bradley Dept. of Electr. & Comput. Eng., Virginia Polytech. Inst. & State Univ., Blacksburg, VA, USA
Volume :
54
Issue :
7
fYear :
2009
fDate :
7/1/2009 12:00:00 AM
Firstpage :
1632
Lastpage :
1637
Abstract :
We investigate the L 2 gain of periodic linear switched systems under fast switching. For systems that possess a suitable notion of a time-average system, we characterize the relationship between the L 2 gain of the switched system and the L 2 gain of its induced time-average system when the switching rate is sufficiently fast. We show that the switched system L 2 gain is in general different from the average system L 2 gain if the input or output coefficient matrix switches. If only the state coefficient matrix switches, the input-output energy gain for a fixed L 2 input signal is bounded by the L 2 gain of the average system as the switching rate grows large. Additionally, for a fixed L 2 input, the maximum pointwise in time difference between the switched and average system outputs approaches zero as the switching rate grows.
Keywords :
linear systems; matrix algebra; periodic control; time-varying systems; L2 gain; fast switching behavior; output coefficient matrix; periodic linear switched systems; state coefficient matrix; time-average system; Attenuation measurement; Communication switching; Lyapunov method; Performance gain; Power semiconductor switches; Riccati equations; Stability; Switched systems; Switching systems; Time varying systems; ${cal L}_{2}$
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2009.2017974
Filename :
5071165
Link To Document :
