Model Decomposition of Weight-Balanced Timed Event Graphs in Dioids: Application to Control Synthesis

For Timed Event Graphs (TEGs), model reference control is a well known approach to stabilize and to improve the performance of a system. This method is based on dioid and residuation theory. In this work, we study model reference control for the class of single-input and single-output (SISO) Weight-Balanced Timed Event Graphs (WBTEGs), which is an extension of TEGs and exhibits event-variant behavior. By modeling the behavior of WBTEGs in a dioid structure, we propose a decomposition of the dynamic behavior into an event-variant and an event-invariant part. We further show that the event-variant part is invertible, hence the problem of model reference control for WBTEGs can be reduced to the case of conventional TEGs