具有周期子系统的非线性大系统向量Lyapunov函数的构造

IF 0.9 4区数学 Q1 Mathematics

Miskolc Mathematical Notes Pub Date : 2023-01-01 DOI:10.18514/mmn.2023.4207

I. Atamas, V. Denysenko, V. Slyn'ko

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引用次数: 0

摘要

．提出了一种构造非线性非自治大系统向量Lyapunov函数的新方法。假设独立子系统为线性周期系统。向量李雅普诺夫函数的分量选择为具有变量矩阵的二次型。这个矩阵是李雅普诺夫矩阵微分方程的近似解。利用Magnus提出的离散化方法和演化算子的表示构造了该解。建立了一类非线性大系统平凡解渐近稳定的充分条件。通过耦合系统稳定性研究实例说明了所得结果的有效性。

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Construction of vector Lyapunov function for nonlinear large-scale system with periodic subsystems

. A new approach for constructing vector Lyapunov function for nonlinear non-autonomous large-scale systems is proposed. It is assumed that independent subsystems are linear periodic systems. The components of the vector Lyapunov function are chosen as a quadratic form with a variable matrix. This matrix is an approximate solution of the Lyapunov matrix differential equation. This solution is constructed using the discretization method and the representation of the evolution operator proposed by Magnus. Sufﬁcient conditions for the asymptotic stability of a trivial solution of a nonlinear large-scale system are established. The effectiveness of obtained results are illustrated by the example of stability investigation for coupled systems.

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来源期刊

Miskolc Mathematical Notes Mathematics-Algebra and Number Theory

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： Miskolc Mathematical Notes, HU ISSN 1787-2405 (printed version), HU ISSN 1787-2413 (electronic version), is a peer-reviewed international mathematical journal aiming at the dissemination of results in many fields of pure and applied mathematics.