Exact model matching of linear time-varying systems

The paper considers the problem of designing a static or a dynamic controller to match exactly the input-output description of a given linear time-varying system to that of a desired model. The proposed approach is based on the concept of algebraic equivalence, the motivation being that if algebraic equivalence of the closed-loop system and the model is secured then the input-output descriptions of the two systems are matched exactly. This approach readily yields the compensating matrices in terms of the algebraic equivalence transformation matrix which is independently determined from a linear system of first-order differential equations. Theorems stating necessary and sufficient conditions for exact model matching are established. The paper consists of the first results in the field of exact model matching of linear time-varying systems.