Stability Analysis for Systems with Time-Varying Delay: Trajectory Based Approach

Frederic Mazenc 1 Michael Malisoff 2 Silviu-Iulian Niculescu 3, 1
1 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 : Recent work by Mazenc and Malisoff provided a trajectory-based approach to proving stability of time-varying systems with time-varying delay. It uses a contraction lemma, instead of Lyapunov-Krasovskii or Razumikhin functions. Here, we use their lemma, and a Lyapunov function for an unde-layed system, to provide a new method to prove stability of linear continuous-time time-varying systems with time-varying bounded delays. No constraint on the upper bound of delay is imposed, nor do we need any differentiability of the delay. Instead, we use an upper bound on an integral average of the delay. We prove input-to-state stability under disturbances.
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Frederic Mazenc, Michael Malisoff, Silviu-Iulian Niculescu. Stability Analysis for Systems with Time-Varying Delay: Trajectory Based Approach. 54th IEEE Conference on Decision and Control (CDC), Dec 2015, Ozaka, Japan. ⟨10.1109/cdc.2015.7402473 ⟩. ⟨hal-01248070⟩

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