Symbolic models for incrementally stable switched systems with aperiodic time sampling

Abstract : In this paper, we consider the problem of symbolic model design for the class of incrementally stable switched systems. Contrarily to the existing results in the literature where switching is considered as periodically controlled, in this paper, we consider aperiodic time sampling resulting either from uncertain or event-based sampling mechanisms. Firstly, we establish sufficient conditions ensuring that usual symbolic models computed using periodic time-sampling remain approximately bisimilar to a switched system when the sampling period is uncertain and belongs to a given interval; estimates on the bounds of the interval are provided. Secondly, we propose a new method to compute symbolic models related by feedback refinement relations to incrementally stable switched systems, using an event-based approximation scheme. For a given precision, these event-based models are guaranteed to enable transitions of shorter duration and are likely to allow for more reactiveness in controller design. Finally, an example is proposed in order to illustrate the proposed results and simulations are performed for a Boost dc-dc converter structure.
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Zohra Kader, Antoine Girard, Adnane Saoud. Symbolic models for incrementally stable switched systems with aperiodic time sampling. 6th IFAC Conference on Analysis and Design of Hybrid System, ADHS 2018, Jul 2018, Oxford, United Kingdom. ⟨hal-01760789⟩

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