Characterizations of J-lossless time-varying systems via the chain scattering approach

In this paper, via the chain scattering formalism, we derive the inequality condition for a bounded I/O operator which is associated with a finite-dimensional linear time-varying system to be lossless or J-lossless. The characterizations for J-losslessness apply to a J-lossless time-varying system which is either exponentially stable, anti-stable or one with a uniform stable/anti-stable decomposition of its state space. Uniform time-varying realizations are considered as they are required for the proof of the necessity of the state space characterizations. The results provide an extension to the state space characterizations of linear time-invariant J-lossless systems which belong to RLinfinity. The characterizations for (J, J')-lossless LTV systems are also derived. (C) 1998 John Wiley & Sons, Ltd.