The Max-Plus-Linear (MPL) system is a state-space description for a certain class of discrete-event-systems that are-linear in max-plus algebra. This paper considers an extended description of MPL systems with a linear parameter varying structure, which is called LPV-MPL systems, and proposes an inverse system of the LPV-MPL system, which calculates the control inputs so that the control outputs should be equal or less than and close to the desired reference signal. The greatest subsolution for a polytopic linear matrix equation is newly introduced for the derivation of the inverse system. The proposed control law can be utilized effectively in the case where the parameters are measured on-line, or the variation of the parameters are scheduled beforehand because it explicitly includes the parameters of controlled MPL systems. A numerical example of the proposed inverse system for a two-inputs, two-outputs production system with four machines is also shown.