Paper Info
Title
Pre-orders for reasoning about stability properties with respect to input of hybrid systems
Abstract
Pre-orders on systems are the basis for abstraction based verification of systems. In this paper, we investigate pre-orders 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 input-to-state stability of continuous systems in terms of the traditional ε-δ definition of stability. We use this as the basis for defining a notion of incremental input-to-state stability of hybrid systems. Next, we present a pre-order on hybrid systems which preserves incremental input-to-state 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 counter-examples to show that weaker notions of input bisimulation with just continuity requirements do not suffice to preserve stability. Finally, we demonstrate that the definitions are useful, by exhibiting concrete abstraction functions which satisfy the definitions of pre-orders.
Year
DOI
Venue
2013
10.1109/EMSOFT.2013.6658602
EMSOFT
Keywords
Field
DocType
reasoning about stability properties,uniform continuity constraint,concrete abstraction function,classical incremental input-to-state stability,traditional ε-δ definition,continuity requirements,bisimulation relations,stability,hybrid system,stability property,verification,abstraction based verification,abstraction,(bi)-simulations,reasoning about programs,stability preservation,bisimulation equivalence,type theory,hybrid system input,preorder definition,classical definition,uniform continuity constraints,superposition type theorem,incremental input-to-state stability,continuity requirement,input bisimulation,continuous systems,bisimulation relation,uniform continuity,abstraction function
Superposition principle,Abstraction,Computer science,Type theory,Algorithm,Theoretical computer science,Uniform continuity,Bisimulation,Hybrid system,Bisimulation equivalence,Distributed computing
Conference
ISBN
Citations 
PageRank 
978-1-4799-1443-2
6
0.48
References 
Authors
16
3
Name
Order
Citations
PageRank
Pavithra Prabhakar121925.69
Jun Liu221520.63
Richard M. Murray3123221223.70