Co-(J'',J)-lossless co-conjugations and co-(J'',J)-lossless factorizations of linear time-varying systems

The notion of co-conjugation for linear time-varying (LTV) systems is introduced. Via the dual chain scattering formalism, we derive the state-space characterizations for an exponential dichotomous co-lossless and co-(J(mq), J(mr))-lossless uniform LTV system and the inequality condition for the associated bounded I/O operators. Uniform time-varying realizations are considered, as they are required for the proof of the necessity of the state-space characterizations. The fundamental operation of co-(J(mq), J(mr))-lossless conjugation is shown to provide a simple way to the co-(J(mq), J(mr))-lossless factorizations of LTV systems, where necessary and sufficient conditions for its existence are given.