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Lyapunov‐Based Stability of Mix‐Valued Logical Networks
Author(s) -
Zhao Jing,
Meng Fanwei,
Liu Zhenbin
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1804
Subject(s) - lyapunov function , stability (learning theory) , probabilistic logic , mathematics , logical conjunction , function (biology) , lyapunov redesign , computer science , mathematical optimization , nonlinear system , physics , quantum mechanics , machine learning , evolutionary biology , biology , programming language , statistics
This paper investigates Lyapunov‐based stability of mix‐valued logical networks. First, we consider the pseudo‐logical function, and give its general logical expression. Second, based on pseudo‐logical functions, we give some definitions on the strict‐Lyapunov function of mix‐valued logical networks and establish a necessary and sufficient condition about the stability. Third, the obtained results are applied to probabilistic logical networks, and a necessary and sufficient condition of globally stability is proposed. Finally, the study of illustrative examples shows that new results presented in this paper work very well.