Performance Evaluation of Switched Discrete Event Systems

Based on max-plus algebra, a class of discrete event processes can be described by linear recursive equations[1]. Such a system exhibits asymptotic periodic behavior, and its performance can be evaluated by calculating the eigenvalue of the system matrix in max-plus algebra. On the other hand, control techniques based on switching among different controllers have been explored extensively in recent years, where they have been shown to achieve better dynamic performance[2]. This paper proposes a new model for a class of switched discrete event systems. Such a model consists of a finite set of discrete event subsystems, and a switching law that orchestrates the switching among them. We show that, the switched system can be transformed into a non-switched system, and under certain conditions, the switched system exhibits asymptotic periodic behavior, and its performance can be evaluated by calculating the eigenvalue of certain matrix in max-plus algebra.