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针对在判断群体系统的稳定性时没有一般的方法和程序构造Lyapunov函数这个难点,利用矩阵范数,孤立子系统的矩阵指数函数与比较原理提出了一类线性时变群体系统平凡解一致稳定,所有解一致有界的充分条件。方便此类群体系统的稳定性分析,为研究其他群体系统稳定性的代数判据提供了理论基础。可以在此基础上,进一步研究一类非线性群体系统稳定性的代数判据。同时,还给出了具体算例,说明所提方法的正确性。此代数判据应用简便,灵活,适于实际应用。
Aiming at the difficulty of constructing Lyapunov function by general methods and procedures in judging the stability of the group system, this paper proposes a class of linear time-varying group systems with uniform stability and stability by using the matrix norm, the exponential function and the comparison principle of the soliton systems. All solutions are well-bounded and sufficient conditions. It is convenient for the stability analysis of such groups to provide a theoretical basis for studying the algebraic criteria of the stability of other groups. Based on this, we can further study the algebraic criteria for the stability of a class of nonlinear population systems. At the same time, a specific example is given to illustrate the correctness of the proposed method. The algebraic criterion is simple, flexible and suitable for practical application.