Stability of Nonlinear Comparison Equations for Discrete Large-Scale Systems

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Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(8): 731-737

Shu Huang. Stability of Nonlinear Comparison Equations for Discrete Large-Scale Systems[J]. Applied Mathematics and Mechanics, 1990, 11(8): 731-737.

Citation:

Shu Huang. Stability of Nonlinear Comparison Equations for Discrete Large-Scale Systems[J]. Applied Mathematics and Mechanics, 1990, 11(8): 731-737.

Citation:

Shu Huang. Stability of Nonlinear Comparison Equations for Discrete Large-Scale Systems[J]. Applied Mathematics and Mechanics, 1990, 11(8): 731-737.

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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