Decay Rate Assignment Through Multiple Spectral Values in Delay Systems

• 成果类型: Article
• 署名作者: Boussaada, Islam; Mazanti, Guilherme; Niculescu, Silviu-Iulian; Michiels, Wim
• 署名单位: Universite Paris Saclay; Inria; Centre National de la Recherche Scientifique (CNRS); KU Leuven
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3447117
• 发表日期: 2025
• 页码: 830-844
• 关键词: Delays; POLYNOMIALS; Linear systems; asymptotic stability; Numerical stability; dynamical systems; systematics; characteristic function; delay; exponential stability; Green-Hille transformation; hypergeometric functions; Kummer functions; partial pole placement

摘要

This article focuses on a spectral property for linear time-invariant dynamical systems represented by delay-differential equations (DDEs) entitled multiplicity-induced-dominancy (MID), which consists, roughly speaking, in the spectral abscissa of the system being defined by a multiple spectral value. More precisely, we focus on the MID property for spectral values with overorder multiplicity, i.e., a multiplicity larger than the order of the DDE. We highlight the fact that a root of overorder multiplicity is necessarily a root of a particular polynomial, called the elimination-produced polynomial, and we address the MID property using a suitable factorization of the corresponding characteristic function involving special functions of Kummer type. Additional results and discussion are provided in the case of the nth order integrator, in particular on the local optimality of a multiple root. The derived results show how the delay can be further exploited as a control parameter and are applied to some problems of stabilization of standard benchmarks with prescribed exponential decay.