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Semitensor Product Approach to Controllability, Reachability, and Stabilizability of Probabilistic Finite Automata

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  • Wenhui Dou
  • Haitao Li
  • Fuad E. Alsaadi

Abstract

This paper proposes a matrix-based approach to investigate the controllability, reachability, and stabilizability of probabilistic finite automata (PFA). Firstly, the state transition probabilistic structure matrix is constructed for PFA, based on which a kind of controllability matrix is defined for PFA. Secondly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of PFA with positive probability by using the controllability matrix. Finally, an illustrate example is given to validate the obtained new results.

Suggested Citation

  • Wenhui Dou & Haitao Li & Fuad E. Alsaadi, 2019. "Semitensor Product Approach to Controllability, Reachability, and Stabilizability of Probabilistic Finite Automata," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-7, April.
    • Handle: RePEc:hin:jnlmpe:8021750
    DOI: 10.1155/2019/8021750
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