Simple Tests for Uniform Exponential Stability of a Linear Delayed Vector Differential Equation

• 成果类型: Article
• 署名作者: Berezansky, Leonid; Diblik, Josef; Svoboda, Zdenek; Smarda, Zdenek
• 署名单位: Ben-Gurion University of the Negev; Brno University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3069901
• 发表日期: 2022
• 页码: 1537-1542
• 关键词: Delays; Stability criteria; asymptotic stability; control theory; Mathematical model; Differential equations; Mechanical variables measurement; Bohl-Perron (BP) method; delay; exponential stability; linear differential system; matrix measure; stability test

摘要

A linear delayed vector equation (x) over dot(t) = Sigma(m)(k=1) A(k)(t)x(h(k)(t)), t is an element of [0,infinity) is investigated, where x = (x(1), ... , x(n))T is an unknown vector function. The system is considered in the most general setting and under weak assumptions about the entries of matrices A(k) and delays h(k). The main result on uniform exponential stability is universal in the sense that it generates a set of 2(m) - 1 independent explicit statements (that can depend on all delays) on uniform exponential stability. The advantages over the existing results are demonstrated. The main tools employed by this article include the Bohl-Perron method, a priori estimates of solutions, and transformations of differential equations.