Year: 2024
Type: article
Abstract: This article focuses on a spectral property for linear time-invariant dynamical systems represented by delay-differential equations (DDEs) entitledmultiplicity-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 theelimination-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$n$th order integrator, in particular on the local optimality of a multiple root. The derived results show how the delay can be further exploited as acontrol parameterand are applied to some problems of stabilization of standard benchmarks with prescribed exponential decay.
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390865693