Abstract: For the off-line controller synthesis problem of discrete event dynamic systems (DEDS), most existing methods are under the assumption that the state-space is finite. For the concurrent DEDS with infite state-space, a Petri Net graph based matrix algebra synthesis method is proposed in this paper. By structural decomposition of Petri Nets, the new method can be used to synthesize the state feedback controllers of a class of DEDS which can be described by structurally no-competing Petri Nets.