When Is σ (A(t)) ⊂ {z ∈ C; < Rz ≤ -α < 0} the Sufficient Condition for Uniform Asymptotic Stability of LTV System (x) over dot = A(t)x?

被引：0

作者：

Vrabel, Robert ^{[1
]}

机构：

[1] Slovak Univ Technol Bratislava, Inst Appl Informat Automat & Mechatron, Bottova 25, Trnava 91701, Slovakia

来源：

MATHEMATICS | 2022年 / 10卷 / 01期

关键词：

linear time-varying system; stability; logarithmic norm; NORM;

D O I：

10.3390/math10010141

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the class of matrix functions A(t) is determined for which the condition that the pointwise spectrum sigma(A(t)) subset of {z is an element of C; Rz <= -alpha} for all t >= t(0) and some alpha > 0 is sufficient for uniform asymptotic stability of the linear time-varying system (x) over dot = A (t) x. We prove that this class contains as a proper subset the matrix functions with the values in the special orthogonal group SO(n).

引用

页数：12

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