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TW 363
Wim Michiels, Sabine Mondie and Dirk Roose
Robust stabilization of time-delay systems with distributed delay control laws:
necessary and sufficient conditions for a safe implementation
Abstract
The instability mechanism of finite spectrum assignment based controllers, when the distributed delay in the control law is approximated with a sum of point-wise delays, is known to be related to the behavior of the essential spectrum of the solution semi-group of neutral functional differential equations. We explain and graphically illustrate with eigenvalue plots that stability may be sensitivity to the type of integration rule used and to infinitesimal perturbations on parameters. These considerations lead to a definition of stability in a robust sense. Unlike previous works on the topic, necessary and sufficient conditions for the stabilizability with the approximated control law, based on this definition, are given. The properties of the obtained stability conditions are discussed and illustrated with some examples, emphasizing the relation with those of static state feedback controllers.
report.pdf / mailto: W. Michiels