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 -