群体系统稳定性的研究现状及线性时变系统的稳定性判定方法

Study on present situation for stability of swarm systems and stability determination method for linear time-variable systems

群体系统的稳定性是研究群体系统其它性能的前提条件,本文阐述了其在当前国内外的研究现状,指出当前研究中存在的问题,并提出可能出现的新的研究方法以及研究方向,如非线性群体系统的稳定性分析,关联函数eij属于何种类型函数的确定等。根据一种M-矩阵的判断方法及P-F定理,通过引入两个正参数iτ和pmin,对Siljak等人提出的系统全局最优稳定性判定定理,系统联结稳定性判定定理加以改进,提出了一种线性时变群体系统的稳定性判定方法。此方法简化了计算系统的复杂性,减少了计算量,从而提高了求解效率,具有实际意义。

The stability of swarm systems is the promise of studing the other nature of the swarm systems.The present situation of the current domestic and foreign study for swarm systems stability is summarized and some problems that exist in the current study are pointed out in this paper.Then,the new methods and directions of research that possibly appear are proposed,such as the stability analysis of the non-linear swarm systems,the style of the correlative function eijet al.According to the determination method of M-matrix and P-F theorem,through the positive parameters τi and pmin,the criterion of the system global optimal stability and the criterion of the connective stability which are proposed by Siljak et al.are improved in this paper.A method of stability analysis for a class of swarm systems is proposed.This method simplifies the complexity of computing system,ruduces the computation load,thus promotes the solution efficiency and has practical significances.