Abstraction based verification of stability of polyhedral switched systems

M. Garcia Soto, P. Prabhakar, Nonlinear Analysis: Hybrid Systems 36 (2020) 100856.

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Author
Garcia Soto, MiriamIST Austria ; Prabhakar, Pavithra
Department
Abstract
This paper presents a novel abstraction technique for analyzing Lyapunov and asymptotic stability of polyhedral switched systems. A polyhedral switched system is a hybrid system in which the continuous dynamics is specified by polyhedral differential inclusions, the invariants and guards are specified by polyhedral sets and the switching between the modes do not involve reset of variables. A finite state weighted graph abstracting the polyhedral switched system is constructed from a finite partition of the state–space, such that the satisfaction of certain graph conditions, such as the absence of cycles with product of weights on the edges greater than (or equal) to 1, implies the stability of the system. However, the graph is in general conservative and hence, the violation of the graph conditions does not imply instability. If the analysis fails to establish stability due to the conservativeness in the approximation, a counterexample (cycle with product of edge weights greater than or equal to 1) indicating a potential reason for the failure is returned. Further, a more precise approximation of the switched system can be constructed by considering a finer partition of the state–space in the construction of the finite weighted graph. We present experimental results on analyzing stability of switched systems using the above method.
Publishing Year
Date Published
2020-01-29
Journal Title
Nonlinear Analysis: Hybrid Systems
Volume
36
Issue
5
Article Number
100856
ISSN
IST-REx-ID

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Garcia Soto M, Prabhakar P. Abstraction based verification of stability of polyhedral switched systems. Nonlinear Analysis: Hybrid Systems. 2020;36(5):100856. doi:10.1016/j.nahs.2020.100856
Garcia Soto, M., & Prabhakar, P. (2020). Abstraction based verification of stability of polyhedral switched systems. Nonlinear Analysis: Hybrid Systems, 36(5), 100856. https://doi.org/10.1016/j.nahs.2020.100856
Garcia Soto, Miriam, and Pavithra Prabhakar. “Abstraction Based Verification of Stability of Polyhedral Switched Systems.” Nonlinear Analysis: Hybrid Systems 36, no. 5 (2020): 100856. https://doi.org/10.1016/j.nahs.2020.100856.
M. Garcia Soto and P. Prabhakar, “Abstraction based verification of stability of polyhedral switched systems,” Nonlinear Analysis: Hybrid Systems, vol. 36, no. 5, p. 100856, 2020.
Garcia Soto M, Prabhakar P. 2020. Abstraction based verification of stability of polyhedral switched systems. Nonlinear Analysis: Hybrid Systems. 36(5), 100856.
Garcia Soto, Miriam, and Pavithra Prabhakar. “Abstraction Based Verification of Stability of Polyhedral Switched Systems.” Nonlinear Analysis: Hybrid Systems, vol. 36, no. 5, Elsevier, 2020, p. 100856, doi:10.1016/j.nahs.2020.100856.

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