The partial model matching problem with stability

The Partial model matching problem has been initially introduced in Emre and Silverman (1980) and amounts to matching the first (k + 1) Markov parameters of the compensated plant with those of the model. We give here an algebraic and structural solution to this problem. Moreover, we give an answer to the stability question, which has remained open since then. As a possibly surprising result, we show that if this Partial problem is solvable, then there always exists a stable solution (provided the plant is stabilizable). We illustrate on a simple example how this objective can be realized in combination with some H_∞-norm attenuation. Limitations for the existence of static state feedback solutions are also discussed.