A descriptor approach to compensating internal models

The compensation of internal model is an approach to reduce the stabilization of a plant augmented with an (unstable) internal model to an equivalent stabilization problem for a fictitious plant, whose complexity is the same as that of the plant itself. This note presents a novel approach to construct this fictitious plant in state space, which results in simpler and more transparent procedures than those previously available. The main idea is to employ descriptor systems formalism, which facilitates manipulating systems with potentially nonproper transfer functions. The proposed procedure includes also an additional degree of freedom, which does not affect the complexity of the solution and can be used to tune its properties.