Global stability at a limit cycle for switched multi‐valued logical networks

This paper mainly studies the problem of global stability at limit cycles for switched multi‐valued logical networks (SMLNs). Firstly, the SMLNs are converted into algebraic forms by using semi‐tensor product of matrices. Then an effective method called digital transformation is used to analyze the structural matrices of the obtained algebraic equations. Based on this method, the global stability at a certain limit cycle for SMLNs, a more general situation, is for the first time studied in this paper, and the relevant necessary and sufficient condition is derived. By dividing the structural matrices of switched multi‐valued logical control networks (SMLCNs) into several blocks, a necessary and sufficient condition for SMLCNs to be globally stabilized to a limit cycle under open‐loop control signals is provided. In addition, due to the use of digital transformations, the stability analysis method established for SMLNs and SMLCNs in this paper is sraightforward and the corresponding computational burden is quite small. Finally, two numerical examples are given to show the effectiveness of the obtained results in this work.

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