离散大系统非线性比较方程的稳定性

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基金项目: 国家自然科学基金资助项目,1880359

Stability of Nonlinear Comparison Equations for Discrete Large-Scale Systems

摘要: 用矢量李雅普诺夫函数解决大系统的稳定性问题必须要判断矢量比较方程的稳定性.对离散系统,过去只研究过线性驻定比较方程的稳定性.本文全面建立了离散非线性驻定比较方程的各种稳定性判别准则,其中渐近稳定的准则既是充分也是必要的,并由此推得了一个用于C₁类函数的准则,两者均可用来判断离散非线性(驻定或非驻定)系统的非指数稳定以至全局非指数稳定.所有准则均具有简单的代数形式,便于应用.

Abstract: On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C₁, is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.

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