Finite Bisimulations of Controllable Linear Systems
Copyright 2003 IEEE. Reprinted from Proceedings of the 42nd IEEE Conference on Decision and Control 2003, Volume 1, pages 634-639.
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Finite abstractions of infinite state models have been critical in enabling and applying formal and algorithmic verification methods to continuous and hybrid systems. This has triggered the study and characterization of classes of continuous dynamics which can be abstracted by finite transition systems. In this paper, we focus on synthesis rather than analysis. In this spirit, we show that given any discrete-time, linear control system satisfying a generic controllability property, and any finite set of observations restricted to the boolean algebra of Brunovsky sets, a finite bisimulation always exists and can be effectively computed.
Paulo Tabuada and George J. Pappas. "Finite Bisimulations of Controllable Linear Systems" Departmental Papers (ESE) (2003).
Available at: http://works.bepress.com/george_pappas/192