TY - GEN
T1 - Extremal storage functions and minimal realizations of discrete-time linear switching systems
AU - Philippe, Matthew
AU - Essick, Ray
AU - Dullerud, Geir
AU - Jungers, Raphael M.
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/12/27
Y1 - 2016/12/27
N2 - We study the p induced gain of discretetime linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every p ≥ 1, the p-gain is exactly characterized through switching storage functions. These functions are shown to be the pth power of a norm. In order to consider general systems, we provide an algorithm for computing minimal realizations. These realizations are rectangular systems, with a state dimension that varies according to the mode of the system. We apply our tools to the study on the of p-gain. We provide algorithms for its approximation, and provide a converse result for the existence of quadratic switching storage functions. We finally illustrate the results with a physically motivated example.
AB - We study the p induced gain of discretetime linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every p ≥ 1, the p-gain is exactly characterized through switching storage functions. These functions are shown to be the pth power of a norm. In order to consider general systems, we provide an algorithm for computing minimal realizations. These realizations are rectangular systems, with a state dimension that varies according to the mode of the system. We apply our tools to the study on the of p-gain. We provide algorithms for its approximation, and provide a converse result for the existence of quadratic switching storage functions. We finally illustrate the results with a physically motivated example.
UR - http://www.scopus.com/inward/record.url?scp=85010818067&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2016.7799119
DO - 10.1109/CDC.2016.7799119
M3 - Conference contribution
AN - SCOPUS:85010818067
T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
SP - 5533
EP - 5538
BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 55th IEEE Conference on Decision and Control, CDC 2016
Y2 - 12 December 2016 through 14 December 2016
ER -