On the control of max-plus linear system in dioid of interval

Many physical problems can be modelled with the max-plus linear system and some results have been obtained. In this paper, first we will give some results and properties about intervals and present the definition and operations of interval matrices, then we will put forward the control problem for max-plus linear systems in interval dioid, in which the state respects the given constraints (i.e. inequality about state variables and interval matrix). Our aim is to find a feedback interval matrix to guarantee the evolution of the system satisfies the restrictions imposed on the state. And we will give a sufficient condition for the existence of the feedback causal interval matrix. In the end, an example illustrates our results.