Partial state estimation in the presence of unknown inputs

We consider the class of linear systems with unknown inputs, and we present an algorithm to determine the part of the state which can be estimated for such systems. This amounts to the determination of the detectable subsystem of maximum order which is free from any unknown input. The procedure to get this subsystem is iterative, and the link between the number of iterations and the interactor matrix of the transfer matrix from unknown inputs to measured outputs is pointed out. The iterative method comes out naturally by relaxing the conditions for the existence of an unknown input observer.