SCIENCE CHINA Information Sciences, Volume 62, Issue 9: 192202(2019) https://doi.org/10.1007/s11432-018-9562-y

A novel matrix approach for the stability and stabilization analysis of colored Petri nets

• AcceptedAug 3, 2018
• PublishedJul 30, 2019
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Abstract

In this study, the stability and stabilization problem of a colored Petri net based on the semi-tensor product of matrices is investigated. First, the marking evolution equation of the colored Petri net in a Boolean algebra framework is established,and the necessary and sufficient condition for the stability of the equilibrium point of the colored Petri net is given. Then, the concept of the pre-$k$ steps reachability set is defined and is used to study the problem of marking feedback stabilization. Some properties of the pre-$k$ steps reachability set are developed. The condition of the stabilization of the colored Petri net is given. The algorithm of the optimal marking feedback controller is designed. The proposed method in this paper could judge the stability and stabilization of the colored Petri net by matrix approach. The obtained results are simple and easy to implement by computer. An example is provided to illustrate the effectiveness of the proposed method.

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• Figure 1

The colored Petri net.

• Figure 2

The state space of the colored Petri net.

• Table 1   Pre-reachability set of $M_{6}$
 3 2 1 0 $M_{4}$,$M_{5}$,$M_{11}$ $M_{1}$,$M_{7}$,$M_{8}$,$M_{9}$ $M_{2}$,$M_{3}$,$M_{6}$,$M_{10}$ $M_{6}$

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