TY - JOUR
T1 - Two classes of passive time-varying well-posed linear systems
AU - Schnaubelt, Roland
AU - Weiss, George
PY - 2010/8
Y1 - 2010/8
N2 - We investigate two classes of time-varying well-posed linear systems. Starting from a time-invariant scattering-passive system, each of the time-varying systems is constructed by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of linear systems are motivated by physical examples such as the electromagnetic field around a moving object. To prove the well-posedness of these systems, we use the Lax-Phillips semigroup induced by a well-posed linear system, as in scattering theory.
AB - We investigate two classes of time-varying well-posed linear systems. Starting from a time-invariant scattering-passive system, each of the time-varying systems is constructed by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of linear systems are motivated by physical examples such as the electromagnetic field around a moving object. To prove the well-posedness of these systems, we use the Lax-Phillips semigroup induced by a well-posed linear system, as in scattering theory.
KW - Lax-Phillips semigroup
KW - Linear time-varying system
KW - Operator semigroup
KW - Scattering passive system
KW - Well-posed linear system
UR - http://www.scopus.com/inward/record.url?scp=79952706403&partnerID=8YFLogxK
U2 - 10.1007/s00498-010-0049-0
DO - 10.1007/s00498-010-0049-0
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AN - SCOPUS:79952706403
SN - 0932-4194
VL - 21
SP - 265
EP - 301
JO - Mathematics of Control, Signals, and Systems
JF - Mathematics of Control, Signals, and Systems
IS - 4
ER -