Two dual classes of time-varying well-posed linear systems constructed from passive systems

G. Weiss, R. Schnaubelt
Proceedings of the 44th IEEE Conference on Decision and Control  
We introduce two classes of well-posed linear timevarying (LTV) systems. Each of these can be constructed easily, starting from a time-invariant scattering-passive system, by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of LTV systems are motivated by physical examples, such as an electromagnetic field around a moving object. To prove the well-posedness of these LTV systems, we use the Lax-Phillips semigroup induced
more » ... semigroup induced by a well-posed linear system, as in scattering theory. We modify this semigroup to obtain a Lax-Phillips type evolution family.
doi:10.1109/cdc.2005.1583102 fatcat:nnhya3rajvecbbqzc52v373iq4