Difference between revisions of "Preorders for Reasoning about Stability Properties with respect to Input of Hybrid Systems"
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Latest revision as of 06:14, 15 May 2016
Pavithra Prabhakar, Jun Liu, Richard M. Murray
International Conference on Embedded Software (EMSOFT)
Preorders on systems are the basis for abstraction based verification of systems. In this paper, we investigate preorders for reasoning about stability with respect to inputs of hybrid systems. First, we present a superposition type theorem which gives a characterization of the classical incremental inputtostate stability of continuous systems in terms of the traditional epsilon/deltadefinition of stability. We use this as the basis for defining a notion of incremental input tostate stability of hybrid systems. Next, we present a preorder on hybrid systems which preserves incremental input tostate stability, by extending the classical definitions of bisimulation relations on systems with input, with uniform continuity constraints. We show that the uniform continuity is a necessary requirement by exhibiting counterexamples to show that weaker notions of input bisimulation with just continuity requirements do not suce to preserve stability. Finally, we demonstrate that the definitions are useful, by exhibiting concrete abstraction functions which satisfy the definitions of preorders.
 Conference Paper: http://www.cds.caltech.edu/~murray/preprints/plm13emsoft_s.pdf
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