Robust compensation of a chattering time-varying input delay with jumps

Delphine Bresch-Pietri 1, 2 Frédéric Mazenc 3, 4 Nicolas Petit 2
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily First-In/First-Out (FIFO). This means that the input signals can be reordered. The feedback law uses the current delay value in the prediction. It does not exactly compensate the delay in the closed-loop dynamics but does not require to predict future delay values, contrary to the conventional prediction technique. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic stabilization of the system state, that is, robust delay compensation, providing that the average L 2-norm of the delay time-derivative over some time-window is sufficiently small and that the average time between two discontinuities (average dwell time) is sufficiently large.
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Delphine Bresch-Pietri, Frédéric Mazenc, Nicolas Petit. Robust compensation of a chattering time-varying input delay with jumps. Automatica, Elsevier, 2018, 92, pp.225-234. ⟨10.1016/j.automatica.2018.03.058 ⟩. ⟨hal-01849024⟩

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