TY - GEN
T1 - On ℓ∞ performance optimization of switched systems
AU - Jiang, Shengxiang
AU - Voulgaris, Petros G.
PY - 2007
Y1 - 2007
N2 - In this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n given linear time invariant (LTI) systems. The interest is placed on minimizing the worst case ℓ∞ -induced norm of this model matching system over all possible switchings. This minimization is performed over all Youla-Kucera parameters Q that switch causally in time over n (stable) LTI systems. For the particular set-up at hand, it is shown that the optimal Youla-Kucera parameter Q need not depend on the switching sequence in the case of partially matched switching, and that it can be obtained as an LTI solution to an associated standard ℓ1 optimization. In the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in linear programming, and an approximate solution with any given precision is possible by finite truncation.
AB - In this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n given linear time invariant (LTI) systems. The interest is placed on minimizing the worst case ℓ∞ -induced norm of this model matching system over all possible switchings. This minimization is performed over all Youla-Kucera parameters Q that switch causally in time over n (stable) LTI systems. For the particular set-up at hand, it is shown that the optimal Youla-Kucera parameter Q need not depend on the switching sequence in the case of partially matched switching, and that it can be obtained as an LTI solution to an associated standard ℓ1 optimization. In the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in linear programming, and an approximate solution with any given precision is possible by finite truncation.
KW - Worst case switching
UR - http://www.scopus.com/inward/record.url?scp=52449131992&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2007.4434484
DO - 10.1109/CDC.2007.4434484
M3 - Conference contribution
AN - SCOPUS:52449131992
SN - 1424414989
SN - 9781424414987
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5011
EP - 5016
BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 46th IEEE Conference on Decision and Control 2007, CDC
Y2 - 12 December 2007 through 14 December 2007
ER -