Data Driven Stability Analysis of Black-box Switched Linear Systems

Joris, Kenanian;Ayca, Balkan;Jungers, Raphaël;Paulo, Tabuada
(2018) 57th IEEE Conference on Decision and Control 2018 — Location: Miami Beach, FL, USA (17.December.2018)

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Authors
  • Joris, Kenanian
    Author
  • Ayca, BalkanUniversity of California, Los Angeles
    Author
  • Jungers, RaphaëlUCLouvain
    Author
  • Paulo, Tabuada
    Author
Abstract
Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius.
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Joris, K., Ayca, B., Jungers, R., & Paulo, T. (2018). Data Driven Stability Analysis of Black-box Switched Linear Systems. 57th IEEE Conference on Decision and Control 2018, Miami Beach, FL, USA. https://hdl.handle.net/2078.5/225531