${cal L}_{2}$ Gain of Periodic Linear Switched Systems: Fast Switching Behavior

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; ${cal L}_{2}$ gain analysis; Fast switching; switched systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2017974

Filename

5071165