Fixed poles in the model matching problem for systems over semirings

In this paper, solution existence conditions for the model matching problem are studied for systems over semirings, which are used in many applications, such as queueing systems, communication networks, and manufacturing systems. The main contribution is the discovery of fixed pole structure in solutions to the model matching problem. This fixed pole structure provides essential information contained in all the solutions to the model matching problem. For a discrete-event dynamic system example, a common Petri net component in the solutions of the model matching problem can be discovered from the fixed pole structure.