(J,J′)-lossless factorization for discrete-time systems

The (J,J')-lossless factorization problem for discrete-time systems is considered using a bilinear transformation approach. Necessary and sufficient conditions for the existence of the (J, J')-lossless factorization are given in terms of two discrete-time algebraic Riccati equations whose solvability can readily be checked. A state-space characterization for the (J: J')-lossless factorization is provided. Compared with the derivation given in Kongprawechnon and Kimura (1996), our solution is more concise and our result takes a simpler form which does not require the system matrix to be non-singular.