Strong Stability Analysis of Linear Delay-Difference Equations With Multiple Time Delays

• 成果类型: Article
• 署名作者: Song, Yunxia; Michiels, Wim; Zhou, Bin; Duan, Guang-Ren
• 署名单位: Harbin Institute of Technology; KU Leuven
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3027660
• 发表日期: 2021
• 页码: 3741-3748
• 关键词: Delay-difference equations; quadratic integral Lyapunov functional; robust strong stability; strong stability

摘要

This article is concerned with the strong stability problem of linear continuous-time delay-difference equations with multiple time delays. A family of linear matrix inequalities (LMIs), indexed by a positive integer k, is derived to assess strong stability. A time-domain interpretation of the proposed LMI-based condition is given in terms of a quadratic integral Lyapunov functional, which allows us to reveal relations with an existing result. The LMI condition can easily be reformulated in a form where the dependence on the coefficients of the delay-difference equation is affine, which is instrumental to establishing a sufficient LMI condition for robust strong stability of delay-difference equations with norm-bounded uncertainty. A necessary and sufficient condition for robust strong stability is also given, in the form of a structured singular value characterization. Examples are given to illustrate the effectiveness of the presented results.