Year: 2024
Type: article
Abstract: . In this article the weak infinite zero structures for linear time-delay systems and related problems are investigated. First, by linking the expansion of the transfer function matrix with output derivatives, a structural algorithm to determine the weak infinite zero structures is established, which is instrumental to derive the Smith–McMillan form at infinity of the transfer function matrix through a novel construction of biproper transformation matrices in the weak sense. The presented algorithm is inspired by Silverman’s algorithm and relies on switching between the frequency-domain and time-domain representations and interpretations. Second, the relationship between the weak infinite zero structures and the leading incomplete relative degrees (LIRD) is revealed by analyzing and comparing the algorithms for their computation. Finally, as an application of these results, the transformed outputs and the weak infinite zero structures are used to design delayed output feedback laws, which naturally generalize so-called proportional-derivative controllers.
DOI: 10.1137/23m1606071
Authors: Lei Zhao, Zhao-Yan Li, Bin Zhou, Wim Michiels
Institutions: Harbin Institute of Technology, KU Leuven
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403379081