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Finite Bisimulations for Switched Linear Systems
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Date
2014-12-01
Author
Aydın Göl, Ebru
Ding, Xuchu
Lazar, Mircea
Belta, Calin
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In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space and a switched linear system with stable subsystems, the proposed algorithm generates the bisimulation quotient in a finite number of steps with the aid of sublevel sets of a polyhedral Lyapunov function. Starting from a sublevel set that includes the origin in its interior, the proposed algorithm iteratively constructs the bisimulation quotient for the region bounded by any larger sublevel set. We show how this bisimulation quotient can be used for synthesis of switching laws and verification with respect to specifications given as syntactically co-safe Linear Temporal Logic formulae over the observed polytopic subsets.
Subject Keywords
Abstractions
,
Formal methods
,
Switched systems
URI
https://hdl.handle.net/11511/46021
Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
DOI
https://doi.org/10.1109/tac.2014.2351653
Collections
Department of Computer Engineering, Article
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BibTeX
E. Aydın Göl, X. Ding, M. Lazar, and C. Belta, “Finite Bisimulations for Switched Linear Systems,”
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, vol. 59, no. 12, pp. 3122–3134, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46021.