Model Matching Problems for Positive Systems

The problem of compensating a given plant by means of a static compensator in such a way that, for any input, the output of the compensated system matches that of a given positive model, when both are initialized at 0, and its state evolves in the positive cone for positive initial conditions and inputs is considered. Under a mild structural assumption for the output-difference system between the plant and the model, a complete characterization of solvability of the problem in terms of necessary and sufficient conditions is obtained by means of structural geometric methods. Solvability conditions are practically checkable by algorithmic procedures and by solving a set of linear inequalities. The problem of asymptotic matching for any initial condition is then considered and solvability is characterized by necessary and sufficient conditions. A necessary condition that is practically checkable is given. Solvability by a dynamic compensator is also studied and a sufficient condition to characterize it is given.