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| DOI：https://doi.org/10.1007/s11768-020-00026-8 |
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| Dynamic output feedback stabilization of deterministic finite automata via the semi‑tensor product of matrices approach |
| Roozbeh Abolpour,Mohsen Raji,Parisa Moradi |
| (School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran) |
| Abstract: |
| This paper deals with the dynamic output feedback stabilization problem of deterministic finite automata (DFA). The static
form of this problem is defined and solved in previous studies via a set of equivalent conditions. In this paper, the dynamic
output feedback (DOF) stabilization of DFAs is defined in which the controller is supposed to be another DFA. The DFA
controller will be designed to stabilize the equilibrium point of the main DFA through a set of proposed equivalent conditions.
It has been proven that the design problem of DOF stabilization is more feasible than the static output feedback (SOF)
stabilization. Three simulation examples are provided to illustrate the results of this paper in more details. The first example
considers an instance DFA and develops SOF and DOF controllers for it. The example explains the concepts of the DOF
controller and how it will be implemented in the closed-loop DFA. In the second example, a special DFA is provided in
which the DOF stabilization is feasible, whereas the SOF stabilization is not. The final example compares the feasibility
performance of the SOF and DOF stabilizations through applying them to one hundred random-generated DFAs. The results
reveal the superiority of the DOF stabilization. |
| Key words: Discrete event dynamic system · Finite automata · Dynamic output feedback stabilization · Semi-tensor product |
