Finite Bisimulations of Controllable Linear Systems
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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.
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Copyright 2003 IEEE. Reprinted from Proceedings of the 42nd IEEE Conference on Decision and Control 2003, Volume 1, pages 634-639. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Copyright 2003 IEEE. Reprinted from Proceedings of the 42nd IEEE Conference on Decision and Control 2003, Volume 1, pages 634-639. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.