Disturbance localization and output deadbeat control through an observer in discrete-time linear multivariable systems

This paper considers the problem of disturbance localization for the system , with disturbance , measurement output , and controlled output . It is shown that the problem is solvable by using an observer if and only if where V^*is the largest ( )-invariant subspace in and 2^*is the least ( )-conditioned invariant subspace containing Im . Also, it is shown that there exists a controller using an observer that achieves simultaneous disturbance localization and output deadbeat control if and only if the system is controllable modulo and, in addition, where O^*is the unknown input unconstructible subspace. A simple algorithm is proposed to design such a controller. This algorithm comprises those of designing the optimal output deadbeat state feedback controller and an unknown input observer.