Randomly switching max-plus linear systems and equivalent classes of discrete event systems

In switching max-plus-linear discrete event systems we can switch between different modes of operation. In each mode the discrete event system is described by a max-plus-linear state space model with different system matrices for each mode. In randomly switching max-plus-linear systems, the switching between the modes can be both deterministic and stochastic. The switching changes the structure of the system, which allows the system to break synchronization and to change the order of events. In this paper two equivalent descriptions for randomly switching max-plus-linear systems will be discussed. Furthermore, we will show that a randomly switching max-plus-linear system can be written as a piecewise affine system or a max-min-plus-scaling system. The last transformation can be established under (rather mild) additional assumptions on the boundedness of state and input.