(J,J´)-lossless factorization approach to H∞ control problems with infinite and finite jω-axis zeros

A (J,J´)-lossless factorization approach to 4-block H^∞ control problems with infinite and finite jω-axis zeros is studied. The (J,J´)-lossless factorization for a 2-block plant, which is constructed by augmentation of observation output, and the dual (J,J´)-lossless factorization for a 2-block plant, which is constructed by an augmentation of control input, are discussed dually to reveal the fundamental structures of H^∞ control problems. The necessary and sufficient conditions for the solvability of the 4-block H ^∞ control problems are proposed via generalized eigenvalue problems, and suitable controllers in descriptor form for the problems are given