Stability crossing curves of SISO systems controlled by delayed output feedback

International audience; This paper focuses on closed-loop stability analysis of a class of linear single- input single-output (SISO) systems subject to delayed output feedback. The considered approach makes use of some geometric arguments in frequency-domain, arguments that simplify the understanding of the delay stabilizing mechanism. More precisely, the geometry of stability crossing curves of the closed-loop system is explicitly characterized (classification, tangent and smoothness, direction of crossing) in the parameter space defined by the pair (gain, delay). Such stability crossing curves divide the corresponding parameter space into different regions, such that, within each region, the number of characteristic roots in the right-half plane is fixed. This naturally describes the regions of (gain, delay)-parameters where the system is stable. Various illustrative examples complete the presentation. Copyright © 2007 Watam Press.