Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays

Autor*innen

• Xu-Guang Li

Reihen

• SpringerBriefs in Elektrotechnik und Computertechnik

Parameter

• Architektur & Städtebau
• Technologie & Industrie

Mehr zum Buch

The authors introduce a new frequency-sweeping framework to address the complete stability problem for time-delay systems with commensurate delays. They present an analytic curve perspective that enhances understanding of spectral properties, particularly the asymptotic behavior of characteristic roots on the imaginary axis and properties invariant to delay parameters. This asymptotic behavior is linked to the novel concept of dual Puiseux series, making frequency-sweeping curves valuable for analyzing general time-delay systems. The comparison between Puiseux and dual Puiseux series yields three significant results: an explicit function for the number of unstable roots that simplifies the analysis and design of time-delay systems, allowing them to be treated somewhat like finite-dimensional systems; a classification of all time-delay systems into three types based on their ultimate stability properties; and a straightforward frequency-sweeping criterion that enables asymptotic behavior analysis of critical imaginary roots for all positive critical delays through observation. Researchers and graduate students in time-delay systems, as well as practitioners in engineering, economics, and life sciences dealing with non-instantaneous transfers, will find these findings beneficial for addressing complex delay-related challenges.

• Sprache: Englisch
• Erscheinungsdatum: 2015
• Einband: Paperback