Simultaneously stabilizing controllers subject to QI subspace constraints

In this paper, we establish a necessary and sufficient condition for the existence of a simultaneously stabilizing controller in the given quadratically invariant (QI) subspace constraints for time-varying linear systems within the framework of nest algebra. Furthermore, based on the bicoprime factorizations, a necessary and sufficient condition is derived for the existence of a stabilizing controller subject to QI subspace constraints. These results hold as well in the time-invariant case.