Towards geometric control of max-plus linear systems with applications to manufacturing systems

The max-plus linear systems have been studied for almost three decades, however, a well-established system theory on such specific systems is still an on-going research. The geometric control theory in particular was proposed as the future direction for max-plus linear systems by Cohen et al. This paper reports upon recent investigations on the disturbance decoupling problem for max-plus linear systems, which is the standard geometric control problem originated by W. M. Wonham. Different concepts of the disturbance decoupling problem are introduced, as well as the corresponding solvability conditions and controller synthesis procedures. The main results can be used in manufacturing systems, queueing networks, and power system networks for fault detection and system breakdown prevention.