Hybridization for stability verification of nonlinear switched systems

M. Garcia Soto, P. Prabhakar, in:, 2020 IEEE Real-Time Systems Symposium, IEEE, 2021, pp. 244–256.

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Conference Paper | Published | English
Author
Garcia Soto, MiriamIST Austria ; Prabhakar, Pavithra
Department
Abstract
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.
Publishing Year
Date Published
2021-02-22
Proceedings Title
2020 IEEE Real-Time Systems Symposium
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.
Page
244-256
Conference
RTTS: Real-Time Systems Symposium
Conference Location
Houston, TX, USA
Conference Date
2020-12-01 – 2020-12-04
eISSN
IST-REx-ID

Cite this

Garcia Soto M, Prabhakar P. Hybridization for stability verification of nonlinear switched systems. In: 2020 IEEE Real-Time Systems Symposium. IEEE; 2021:244-256. doi:10.1109/RTSS49844.2020.00031
Garcia Soto, M., & Prabhakar, P. (2021). Hybridization for stability verification of nonlinear switched systems. In 2020 IEEE Real-Time Systems Symposium (pp. 244–256). Houston, TX, USA : IEEE. https://doi.org/10.1109/RTSS49844.2020.00031
Garcia Soto, Miriam, and Pavithra Prabhakar. “Hybridization for Stability Verification of Nonlinear Switched Systems.” In 2020 IEEE Real-Time Systems Symposium, 244–56. IEEE, 2021. https://doi.org/10.1109/RTSS49844.2020.00031.
M. Garcia Soto and P. Prabhakar, “Hybridization for stability verification of nonlinear switched systems,” in 2020 IEEE Real-Time Systems Symposium, Houston, TX, USA , 2021, pp. 244–256.
Garcia Soto M, Prabhakar P. 2021. Hybridization for stability verification of nonlinear switched systems. 2020 IEEE Real-Time Systems Symposium. RTTS: Real-Time Systems Symposium, 244–256.
Garcia Soto, Miriam, and Pavithra Prabhakar. “Hybridization for Stability Verification of Nonlinear Switched Systems.” 2020 IEEE Real-Time Systems Symposium, IEEE, 2021, pp. 244–56, doi:10.1109/RTSS49844.2020.00031.
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