Abstract: Modeling and reachability of a class of Petri net systems (PNSs) by using the semi-tensor product of matrices (STP) was investigated. First, the dynamics of PNSs, by resorting to STP, are converted into a discrete-time bilinear equation. Second, the transition-state adjacency matrix of the PNSs is defined, several necessary and sufficient conditions are obtained for the reachability of the PNSs by means of this bilinear equation and transition-state adjacency matrix. A new algorithm is also designed to find all of the firing sequences of any two reachable states. Finally, an example is presented to illustrate the theoretical results.

Key words: Petri net systems, reachability, the semi-tensor product of matrices, transition-state transfer matrix, transition-state adjacency matrix