(J,J')-LOSSLESS FACTORIZATION FOR DESCRIPTOR SYSTEMS

The (J, J')-lossless factorization for descriptor systems based on the theory of conjugation is studied. The results on (J, J')-lossless fac torization for proper functions are extended to descriptor systems, an d those on J-lossless factorization for square matrices are extended t o nonsquare cases. Since (J, J')-lossless factorization contains both the inner-outer factorization and the Wiener-Hopf spectral factorizati on as special cases, and the descriptor system contains the state-spac e system as a special case, the results obtained here unify the previo us results on factorization problems. Also, (J, J')-lossless factoriza tion can be used to solve 4-block H(infinity) control problems with jo mega-axis zeros.