THE PARTIAL MODEL-MATCHING PROBLEM WITH STABILITY

The Partial model matching problem has been initially introduced in Em re and Silverman (1980) and amounts to matching the first (k + 1) Mark ov parameters of the compensated plant with those of the model. We giv e 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 Part ial problem is solvable, then there always exists a stable solution (p rovided the plant is stabilizable). We illustrate on a simple example how this objective can be realized in combination with some H(infinity )-norm attenuation. Limitations for the existence of static state feed back solutions are also discussed.