Additive Decomposition and its applications to internal-model-based tracking

The proposed additive decomposition is a general way to decompose an original system into two simpler systems, helping designers to analyze the original problem more explicitly. To demonstrate the effectiveness of additive decomposition, we apply it to the internal-model-based tracking problem. By this means, the tracking problem for the original system is decomposed into two subproblems: the tracking problem for a linear time-invariant `primary' system and the stabilization problem for a `secondary' system. Moreover, the former system is independent of the latter. Therefore, various special tools for analyzing linear systems can be applied to the first subproblem which is helpful to the designers. Two application examples are given to illustrate the effectiveness of the proposed additive decomposition.