The time-varying discrete four block Nehari problem: A generalized Popov-Yakubovich type approach

The paper provides necessary and sufficient solvability conditions for the time-variant discrete four block Nehari problem in terms of the existence of the stabilizing solutions to two coupled Riccati equations. A parametrization of the class of all solutions is also given. The results are easily obtained from a signature condition — a generalized Popov Yakubovich type argument-imposed on an appropiate rational node. The present development may be seen as an alternative of the theory developed by Gohberg, Kaashoek and Woerdeman [15].