On characterizations of the input-to-state stability property
Systems & Control Letters
Model checking
Communication and Concurrency
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EMSOFT '02 Proceedings of the Second International Conference on Embedded Software
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HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
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CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
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RTSS '03 Proceedings of the 24th IEEE International Real-Time Systems Symposium
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ACM Transactions on Embedded Computing Systems (TECS)
Approximate Simulation Relations for Hybrid Systems
Discrete Event Dynamic Systems
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HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Input-to-state stability and interconnections of discontinuous dynamical systems
Automatica (Journal of IFAC)
Epsilon-Tubes and Generalized Skorokhod Metrics for Hybrid Paths Spaces
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
On bicontinuous bisimulation and the preservation of stability
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Pre-orders for reasoning about stability
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Input/output-to-state stability and state-norm estimators for switched nonlinear systems
Automatica (Journal of IFAC)
Input-output robustness for discrete systems
Proceedings of the tenth ACM international conference on Embedded software
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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.