混合值逻辑网络的集合稳定

Set stability of mix-valued logical networks

逻辑系统的集合稳定性是基于全局稳定性给出的概念,它研究系统是否能够稳定到某一个状态集合.对此,主要研究混合值逻辑网络的集合稳定性.首先,介绍混合值逻辑网络,并运用矩阵半张量积将其转化为离散代数系统以便于进一步研究;然后,介绍系统不变子集的概念,并给出寻找最大不变子集的方法,在此基础上给出系统集合稳定的充分必要条件;最后,考察系统部分状态的一致稳定性,并将其转化为系统的集合稳定问题,同时通过数值例子加以验证.

On the basis of the global stability of mix-valued logical networks, the concept of set stability is preposed,which determines whether a given system converges to a given subset. This paper investigates the set stability of mixvalued logical networks. Firstly, the mix-valued logical networks are introduced, which are translated into discrete linear dynamic equations by using the semi-tensor product of matrices. Then, the concept of invariant subsets is introduced, and a method of searching for the largest invariant subset is proposed. Based on above, a necessary and sufficient condition for set stability of the concerned networks is developed. Finally, the stability of partial states is proposed, and is converted to the study of set stability for a certain subset. A numerical example is given to illustrate the effectiveness of the obtained results.