TY - GEN
T1 - Shift-invariant representation of two periodic system classes defined over doubly-infinite continuous time
AU - Khong, Sei Zhen
AU - Cantoni, Michael
PY - 2010/1/1
Y1 - 2010/1/1
N2 - This paper considers an isomorphism introduced by Bamieh et. al. in [1], to construct shift-invariant representations, over the same'time-lifted' system class, for two classes of linear periodically time-varying (LPTV) systems. Specifically, we consider the class of finite-dimensional linear time-invariant (LTI) systems, characterised by a rational frequency-domain symbol, and a class of LPTV systems with sampled-data structure. Such systems appear together in problems of sampled-data approximation, for example. We study them here in terms of mappings between finite-energy signals defined over the doubly-infinite continuous-time axis (-∞,∞), which arises when working with the ν-gap metric to gauge approximation error for such problems. A complication within this context stems from the absence of an integral-operator input-output representation for every system in the LPTV classes considered. We resolve this issue by working with the graph representation of the systems involved.
AB - This paper considers an isomorphism introduced by Bamieh et. al. in [1], to construct shift-invariant representations, over the same'time-lifted' system class, for two classes of linear periodically time-varying (LPTV) systems. Specifically, we consider the class of finite-dimensional linear time-invariant (LTI) systems, characterised by a rational frequency-domain symbol, and a class of LPTV systems with sampled-data structure. Such systems appear together in problems of sampled-data approximation, for example. We study them here in terms of mappings between finite-energy signals defined over the doubly-infinite continuous-time axis (-∞,∞), which arises when working with the ν-gap metric to gauge approximation error for such problems. A complication within this context stems from the absence of an integral-operator input-output representation for every system in the LPTV classes considered. We resolve this issue by working with the graph representation of the systems involved.
KW - Doubly-infinite time
KW - Multiplication operators
KW - Periodic systems
KW - Sampled-data systems
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M3 - Conference contribution
AN - SCOPUS:78649270936
SN - 9784907764364
T3 - Proceedings of the SICE Annual Conference
SP - 197
EP - 204
BT - Proceedings of SICE Annual Conference 2010, SICE 2010 - Final Program and Papers
PB - Society of Instrument and Control Engineers (SICE)
ER -