Stability analysis of singularly perturbed switched and impulsive linear systems

Abstract : This paper proposes a new methodology for stability analysis of singularly perturbed linear systems whose dynamics is affected by switches and state jumps. The overall problem is formulated in the framework of hybrid singularly perturbed systems and we use Lyapunov-based techniques to investigate its stability. We emphasize that, beside the stability of slow and fast dynamics, we need a dwell-time condition to guarantee the overall singularly perturbed system is globally asymptotically stable. Furthermore, we characterize this dwell-time as the sum of one term related to the stabilization of systems evolving on one timescale (slow dynamics) and one term of the order of the parameter defining the ratio between the timescales. As highlighted in the paper the second term is required to compensate the effect of the jumps introduced in the state of the boundary layer system by the switches and impulses affecting the overall dynamics. Some numerical examples illustrates our results.
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Jihene Ben Rejeb, Irinel-Constantin Morarescu, Antoine Girard, Jamal Daafouz. Stability analysis of singularly perturbed switched and impulsive linear systems. 55th IEEE Conference on Decision and Control, CDC 2016, Dec 2016, Las Vegas, NV, United States. ⟨10.1109/cdc.2016.7799117 ⟩. ⟨hal-01379136⟩

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