---
_id: '9202'
abstract:
- lang: eng
  text: We propose a novel hybridization method for stability analysis that over-approximates
    nonlinear dynamical systems by switched systems with linear inclusion dynamics.
    We observe that existing hybridization techniques for safety analysis that over-approximate
    nonlinear dynamical systems by switched affine inclusion dynamics and provide
    fixed approximation error, do not suffice for stability analysis. Hence, we propose
    a hybridization method that provides a state-dependent error which converges to
    zero as the state tends to the equilibrium point. The crux of our hybridization
    computation is an elegant recursive algorithm that uses partial derivatives of
    a given function to obtain upper and lower bound matrices for the over-approximating
    linear inclusion. We illustrate our method on some examples to demonstrate the
    application of the theory for stability analysis. In particular, our method is
    able to establish stability of a nonlinear system which does not admit a polynomial
    Lyapunov function.
acknowledgement: Miriam Garc´ıa Soto was partially supported by the Austrian Science
  Fund (FWF) under grant Z211-N23 (Wittgenstein Award). Pavithra Prabhakar was partially
  supported by NSF CAREER Award No. 1552668, NSF Award No. 2008957 and ONR YIP Award
  No. N000141712577.
article_processing_charge: No
author:
- first_name: Miriam
  full_name: Garcia Soto, Miriam
  id: 4B3207F6-F248-11E8-B48F-1D18A9856A87
  last_name: Garcia Soto
  orcid: 0000-0003-2936-5719
- first_name: Pavithra
  full_name: Prabhakar, Pavithra
  last_name: Prabhakar
citation:
  ama: 'Garcia Soto M, Prabhakar P. Hybridization for stability verification of nonlinear
    switched systems. In: <i>2020 IEEE Real-Time Systems Symposium</i>. IEEE; 2020:244-256.
    doi:<a href="https://doi.org/10.1109/RTSS49844.2020.00031">10.1109/RTSS49844.2020.00031</a>'
  apa: 'Garcia Soto, M., &#38; Prabhakar, P. (2020). Hybridization for stability verification
    of nonlinear switched systems. In <i>2020 IEEE Real-Time Systems Symposium</i>
    (pp. 244–256). Houston, TX, USA : IEEE. <a href="https://doi.org/10.1109/RTSS49844.2020.00031">https://doi.org/10.1109/RTSS49844.2020.00031</a>'
  chicago: Garcia Soto, Miriam, and Pavithra Prabhakar. “Hybridization for Stability
    Verification of Nonlinear Switched Systems.” In <i>2020 IEEE Real-Time Systems
    Symposium</i>, 244–56. IEEE, 2020. <a href="https://doi.org/10.1109/RTSS49844.2020.00031">https://doi.org/10.1109/RTSS49844.2020.00031</a>.
  ieee: M. Garcia Soto and P. Prabhakar, “Hybridization for stability verification
    of nonlinear switched systems,” in <i>2020 IEEE Real-Time Systems Symposium</i>,
    Houston, TX, USA , 2020, pp. 244–256.
  ista: 'Garcia Soto M, Prabhakar P. 2020. Hybridization for stability verification
    of nonlinear switched systems. 2020 IEEE Real-Time Systems Symposium. RTTS: Real-Time
    Systems Symposium, 244–256.'
  mla: Garcia Soto, Miriam, and Pavithra Prabhakar. “Hybridization for Stability Verification
    of Nonlinear Switched Systems.” <i>2020 IEEE Real-Time Systems Symposium</i>,
    IEEE, 2020, pp. 244–56, doi:<a href="https://doi.org/10.1109/RTSS49844.2020.00031">10.1109/RTSS49844.2020.00031</a>.
  short: M. Garcia Soto, P. Prabhakar, in:, 2020 IEEE Real-Time Systems Symposium,
    IEEE, 2020, pp. 244–256.
conference:
  end_date: 2020-12-04
  location: 'Houston, TX, USA '
  name: 'RTTS: Real-Time Systems Symposium'
  start_date: 2020-12-01
date_created: 2021-02-26T16:38:24Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2025-04-15T06:25:57Z
day: '01'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1109/RTSS49844.2020.00031
external_id:
  isi:
  - '000680435100021'
file:
- access_level: open_access
  checksum: 8f97f229316c3b3a6f0cf99297aa0941
  content_type: application/pdf
  creator: mgarcias
  date_created: 2021-02-26T16:38:14Z
  date_updated: 2021-02-26T16:38:14Z
  file_id: '9203'
  file_name: main.pdf
  file_size: 1125794
  relation: main_file
file_date_updated: 2021-02-26T16:38:14Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Submitted Version
page: 244-256
project:
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z211
  name: Formal methods for the design and analysis of complex systems
publication: 2020 IEEE Real-Time Systems Symposium
publication_identifier:
  eisbn:
  - '9781728183244'
  eissn:
  - 2576-3172
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hybridization for stability verification of nonlinear switched systems
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2020'
...