The partial model matching or partial disturbance rejection problem: geometric and structural solutions

The partial model matching problem (or equivalently, the partial disturbance rejection problem) is revisited. It has been initially introduced in Emre and Silverman (1980) and amounts to matching the first k Markov parameters of the plant with those of the model. This obviously finds all its interest when no solution exists to the exact problem. The authors give both geometric and structural solutions to these problems. The geometric solution is in terms of the steps of the well known supremal output nulling controlled invariant subspace algorithm. The structural conditions amount to comparing some list of integers, namely some orders of zeros at infinity