A necessary and sufficient condition for parameter insensitive disturbance-rejection problem with state feedback

In this paper a necessary and sufficient condition for a parameter insensitive disturbance-rejection problem with state feedback which was pointed out as an open problem by Bhattacharyya to be solvable is proved. A constructive algorithm of simultaneously (A,B)(A,B)-invariant subspaces for a finite-number of linear systems and a relationship between simultaneously (A,B)(A,B)-invariant subspaces and generalized (A,B)(A,B)-invariant subspaces play an important role to prove the main result.