Output deadbeat control of discrete-time multivariable systems

A new algorithm is presented to compute output deadbeat controls for linear multivariable systems. The algorithm, based on quadratic optimization with no cost on control (cheap control), is numerically stable and covers the most general cases. The resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time. The central part of the algorithm is the construction of the non-unique state cost matrix. Two alternatives are presented having different complexities and resulting in solutions having different properties.