Fixed Poles in the Model Matching Problem for Systems over Semirings

In this paper, we study the model matching problem for systems over semirings, which are used in many applications, such as queueing systems, communication networks, and manufacturing systems. The main contribution of this paper is the discovery of fixed pole structure of solutions to the model matching problem. This fixed pole structure provides essential information contained in the solutions to the model matching problem. For a discrete event dynamic system, a common Petri net component in the solutions to the model matching problem can be discovered from the fixed pole structure. Keywords: Model matching problem, discrete-event dynamic systems, max-plus algebra, fixed poles.