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 x(i + 1) = Ax(i) + Bu(i) + Dd(i), y(i) = Cx(i), w(i) = Ex(i), with disturbance d(i), measurement output y(i), and controlled output w(i). It is shown that the problem is solvable by using an observer if and only if v*?l* where V* is the largest (A, B)-invariant subspace in ker E and L* is the least (A, ker C)-conditioned invariant subspace containing Im D. 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 ker E and, in addition, v* ? o* where O * is the unknown input unconstructible subspace. A simple algorithm is proposed to design such a controller. This algorithm comprlses those of designing the optimal output deadbeat state feedback controller and an unknown input observer. © 1979 IEEE