Construction of Diagonal Lyapunov–Krasovskii Functionals for a Class of Positive Differential-Algebraic Systems

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-09-11 DOI:10.1134/s001226612405001x

A. Yu. Aleksandrov

引用次数: 0

Abstract

A coupled system describing the interaction of a differential subsystem with nonlinearities of a sector type and a linear difference subsystem is considered. It is assumed that the system is positive. A diagonal Lyapunov–Krasovskii functional is constructed, and conditions are determined under which the absolute stability of the system can be proved with the use of such a functional. In the case of power-law nonlinearities, estimates for the rate of convergence of the solution to the origin are obtained. The stability of the corresponding system with parameter switching is analyzed. Sufficient conditions guaranteeing the asymptotic stability of the zero solution for any admissible switching law are obtained.

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构建一类正微分代数系统的对角线 Lyapunov-Krasovskii 函数

摘要本文考虑了一个耦合系统，该系统描述了一个扇形非线性微分子系统与一个线性差分子系统之间的相互作用。假定系统为正。构建了一个对角 Lyapunov-Krasovskii 函数，并确定了使用该函数证明系统绝对稳定的条件。在幂律非线性的情况下，得到了解向原点收敛速度的估计值。分析了具有参数切换的相应系统的稳定性。得到了保证任何可接受的切换规律的零点解的渐近稳定性的充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.