On the pole placement of scalar linear delay systems with two delays

Abstract

This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the characteristic roots are explored, as well as the dominancy of such roots compared with the spectrum localization. As a by-product of the analysis, the pole placement issue is revisited with more emphasis on the role of the delays as control parameters in defining a partial pole placement guaranteeing the closed-loop stability with an appropriate decay rate of the corresponding dynamical system.

References in corpus (4)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Multiplicity-induced-dominancy for delay-differential equations of retarded type
• The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions
• Partial Pole Placement via Delay Action: A Python Software for Delayed Feedback Stabilizing Design

Cited by in corpus (1)

• A novel necessary and sufficient condition for the stability of $2\times 2$ first-order linear hyperbolic systems