Stability of Planar Switched Systems under Delayed Event Detection

Legat, Benoît;Gomes, Cláudio Ângelo Gonçalves;Karalis, Paschalis;Jungers, Raphaël;Hans Vangheluwe;et.al.
(2020) 59th IEEE Conference on Decision and Control — Location: Virtual (14.December.2020)

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Authors
  • Legat, Benoîtorcid-logoUCLouvain
    Author
  • Gomes, Cláudio Ângelo GonçalvesAarhus University
    Author
  • Karalis, PaschalisCadence Design Systems
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  • Jungers, RaphaëlUCLouvain
    Author
  • Hans VangheluweUniversity of Antwerp
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Abstract
In this paper, we analyse the impact of delayed event detection on the stability of a 2-mode planar hybrid automata. We consider hybrid automata with a unique equilibrium point for all the modes, and we find the maximum delay that preserves stability of that equilibrium point. We also show for the class of hybrid automata treated that the instability of the equilibrium point for the equivalent hybrid automaton with delay in the transitions is equivalent to the existence of a closed orbit in the hybrid state space, a result that is inspired by the Joint Spectral Radius theorem. This leads to an algorithm for computing the maximum stable delay exactly. Other potential applications of our technique include co-simulation, networked control systems and delayed controlled switching with a state feedback control.
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Legat, B., Gomes, C. Â. G., Karalis, P., Jungers, R., Navarro-López, E. M., & Hans Vangheluwe. (2020). Stability of Planar Switched Systems under Delayed Event Detection. Accepted/in-press. 59th IEEE Conference on Decision and Control, Virtual. https://hdl.handle.net/2078.5/274580