Local stabilization of multi-valued logical control networks via state feedback

A more general stabilization problem of k-valued logical control networks (LCNs) is presented and a reverse-transfer (RT) method is proposed to investigate this problem. Firstly, the RT method is introduced and the concept of stabilizability of k-valued LCNs is generalized. Secondly, using the RT method, some equivalent criteria are proved for the largest stability domain of a fixed point of a k-valued LCN under a constant control. Then some necessary and sufficient local/global stabilizability conditions are derived directly. Based on the local stabilizability condition, a constructive method of designing state feedback stabilizers for k-valued LCNs is provided. Thirdly, according to the results obtained above, some algorithms are developed. Finally, an example is given to show the significance of our proposed problem and the effectiveness of our results.