40 Years of the Direct Matrix-Valued Lyapunov Function Method (Review)*

被引：4

作者：

Martynyuk, A. A. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, SP Timoshenko Inst Mech, 3 Nesterov St, UA-03057 Kiev, Ukraine

来源：

INTERNATIONAL APPLIED MECHANICS | 2020年 / 56卷 / 03期

关键词：

matrix-valued Lyapunov function method; comparison principle; large-scale dynamic systems; stability; asymptotic stability; instability; polystability; LARGE-SCALE SYSTEMS; UNIFORM ASYMPTOTIC STABILITY; SINGULARLY PERTURBED SYSTEMS; STRUCTURAL PERTURBATIONS; NONLINEAR-SYSTEMS; POLYSTABILITY; MOTION;

D O I：

10.1007/s10778-020-01013-x

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

This review presents the main ideas and results of the development of the direct matrix-valued Lyapunov function method for studying the stability of continuous, singularly perturbed, and stochastic systems of equations of perturbed motion. Sufficient conditions of various types of stability for these systems of equations are expressed in terms of the properties of special matrices, which are obtained by constructing matrix-valued Lyapunov functions and evaluating their full derivatives. The equations of motion of an orbital astronomical observatory, the equations of motion of the generators of a large-scale power system, the three-component Lurie-Postnikov system, and others are applications of the results obtained.

引用

页码：253 / 325

页数：73

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[1] 40 Years of the Direct Matrix-Valued Lyapunov Function Method (Review)*
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