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Preorders for Reasoning about Stability Properties with respect to Input of Hybrid Systems 
Abstract 
Preorders on systems are the basis for ab … 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. ich satisfy the definitions of preorders. +


Authors  Pavithra Prabhakar, Jun Liu, Richard M. Murray + 
ID  2013r + 
Source  International Conference on Embedded Software (EMSOFT) + 
Tag  plm13emsoft + 
Title  Preorders for Reasoning about Stability Properties with respect to Input of Hybrid Systems + 
Type  Conference Paper + 
Categories  Papers 
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15 May 2016 06:14:58 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/plm13emsoft_s.pdf + 
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Preorders for Reasoning about Stability Properties with respect to Input of Hybrid Systems +  Title 
