116 research outputs found
Stabilization of time-delay systems with a controlled time-varying delay and applications
International audienceWe study the stability of a linear system with a pointwise, time-varying delay. We assume that the delay varies around a nominal value in a deterministic way and investigate the influence of this variation on stability. More precisely we are interested in characterizing situations where the time-varying delay system is stable, whereas the system with constant delay is unstable. Our approach consists of relating the stability properties of a system with a fast varying point-wise delay with these of a time-invariant system with a distributed delay. Then we can use frequency domain methods to analyze the problem and to derive stability criteria. The results are first illustrated with two theoretical examples. Then, we study a model of a variable speed rotating cutting tool. Based on the developed theory, we thereby provide both a theoretical explanation and a quantitative analysis tool for the beneficial effect of a variation of the machine speed on enhancing stability properties, which was reported in the literature
Transit times and mean ages for nonautonomous and autonomous compartmental systems
We develop a theory for transit times and mean ages for nonautonomous
compartmental systems. Using the McKendrick-von F\"orster equation, we show
that the mean ages of mass in a compartmental system satisfy a linear
nonautonomous ordinary differential equation that is exponentially stable. We
then define a nonautonomous version of transit time as the mean age of mass
leaving the compartmental system at a particular time and show that our
nonautonomous theory generalises the autonomous case. We apply these results to
study a nine-dimensional nonautonomous compartmental system modeling the
terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford
approach (CASA) model, and we demonstrate that the nonautonomous versions of
transit time and mean age differ significantly from the autonomous quantities
when calculated for that model
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