Partial and Global Stabilization at An Attractor for k-valued Logical Control Networks

Abstract

In this paper, the partial and global stability (stabilization) for a class of k-valued logical (control) networks at one of attractors (point attractors or dynamic attractors) are investigated. To address such issues, a so-called “digital transformation approach” has been introduced. Firstly, the concepts of partial stability (and stabilization) of k-valued logical (control) networks are extended from a point attractor to a dynamic attractor. Secondly, based on the semi-tensor product method, the remainder operation and the digital transformation method, the necessary and sufficient conditions for the partial and global stability (stabilization) of k-valued logical (control) networks (with given state feedback) at an attractor are obtained. Finally, examples are given to demonstrate the feasibility of the proposed techniques.