Decoupling problems for switching linear systems without knowledge of the switching signal

The disturbance decoupling problem is considered in the framework of switching linear systems assuming that no information on the actual value of the switching signal or on the current mode of the system is available. By introducing the novel notion of strong conditioned invariant subspace, the solvability of the problem is completely characterized by means of necessary and sufficient conditions. Constructive procedures to check the solvability conditions and to construct solutions, if any exists, are given.