Two classes of passive time-varying well-posed linear systems |
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Authors: | Roland Schnaubelt George Weiss |
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Affiliation: | 1. Department of Mathematics, Institute of Analysis, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany 2. Department of Electrical Engineering-Systems, Tel Aviv University, 69978, Ramat Aviv, Israel
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Abstract: | 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. |
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