(J, J )-lossless conjugations, (J,J )-lossless factorizations and chain scattering approach to time-varying H control: One and two-block cases

) ) ( ( J J J J Using the notions of,-lossless conjugations and,-lossless factorizations, H the one and two-block linear time-varying infinite horizon standard control problem is solved by means of the chain scattering formalism in this paper. The solutions are shown to exist in the form of non-negative definite Lyapunov stabilizing solutions to two matrix differential Riccati equations and satisfying a spectral radius coupling condition. In addition, a state-space proof of the crucial timeJ H varying-lossless embedding theorem in is also shown by exploiting the cascading structure of the chain scattering formalism and with the standard assump) ( J J tions on the plant, a proof of necessity of,-lossless factorization is also given H for the solvability of the control problem.