| Destabilizing Effects of Small Time-Delays on Feedback Controlled Descriptor Systems (2007) | |||||||||||||||||
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| : In the last 15 years the problems of stabilizability and stabilization of descriptor systems have received considerable attention. In this paper it will be shown that if the open-loop system exhibits impulsive behaviour, then the stability of the closedloop system is extremely sensitive to small delays. More precisely, if F is the feedback which leads to a stable and impulsive-free closed-loop system, then there exist numbers " j ? 0 and s j 2 C with lim j!1 " j = 0 and lim j!1 Re s j = +1 and such that the delayed closed-loop system obtained by applying the feedback u(t) = Fx(t \Gamma " j ) has a pole at s j . Keywords: Descriptor systems; Exponential stability; Small time delays; Robustness; Transfer function matrices. AMS subject classifications: 15A18, 15A54, 34A09, 93B35, 93D09, 93D15. This work was supported by British Council/DAAD ARC (Project 464), the Human and Capital Mobility programme (Project number CHRX-CT-93-0402) and NATO (Grant CRG 950179). y Email: hl@maths.b... | |||||||||||||||||
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