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 -