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

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

A. Yu. Aleksandrov

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引用次数: 0

摘要

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

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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