CONSTRUCTION OF VECTOR LYAPUNOV FUNCTION FOR NONLINEAR LARGE-SCALE SYSTEM WITH PERIODIC SUBSYSTEMS

被引：0

作者：

Atamas, Ivan ^{[1
]}

Denysenko, Viktor ^{[2
]}

Slyn'ko, Vitalii ^{[3
]}

机构：

[1] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany

[2] Bohdan Khmelnytsky Natl Univ Cherkasy, Dept Econ & Business Modeling, UA-18031 Cherkassy, Ukraine

[3] Univ Wurzburg, Inst Math, Emil F Str 40, D-97074 Wurzburg, Germany

来源：

MISKOLC MATHEMATICAL NOTES | 2023年 / 24卷 / 02期

关键词：

vector Lyapunov function; asymptotic stability; discretization method; comparison method; nonlinear nonautonomous large-scale systems; STABILITY; STABILIZATION;

D O I：

10.18514/MMN.2023.4207

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：611 / 624

页数：14

共 18 条

[1] Robust Stability and Stabilization of Linear Switched Systems With Dwell Time [J].