conference paper published yes Miriam Garcia Soto author 4B3207F6-F248-11E8-B48F-1D18A9856A870000-0003-2936-5719 Pavithra Prabhakar author ToHe department RTTS: Real-Time Systems Symposium Formal methods for the design and analysis of complex systems project 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. https://research-explorer.ista.ac.at/download/9202/9203/main.pdf application/pdfno IEEE2020Houston, TX, USA eng 2576-3172 00068043510002110.1109/RTSS49844.2020.00031 244-256 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. 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>. 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> 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> M. Garcia Soto, P. Prabhakar, in:, 2020 IEEE Real-Time Systems Symposium, IEEE, 2020, pp. 244–256. 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>. 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. 92022021-02-26T16:38:24Z2025-04-15T06:25:57Z