Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Ergodic Control of Switching Diffusions
SIAM Journal on Control and Optimization
AMAST '00 Proceedings of the 8th International Conference on Algebraic Methodology and Software Technology
An Algorithm for Quantitative Verification of Probabilistic Transition Systems
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
Towars a Theory of Stochastic Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Hybrid Systems: Computation and Control: 7th International Workshop, Hscc 2004, Philadelphia, Pa, Usa, March 2004: Proceedings (Lecture Notes in Computer Science, 2993)
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
Hybrid Systems: Computation and Control: 8th International Workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005, Proceedings (Lecture Notes in Computer Science)
Polynomial stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Bisimulation for communicating piecewise deterministic markov processes (CPDPs)
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Approximate Simulation Relations for Hybrid Systems
Discrete Event Dynamic Systems
Robust test generation and coverage for hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Safety verification for probabilistic hybrid systems
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
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This paper discusses a notion of approximate abstraction for linear stochastic hybrid automata (LSHA). The idea is based on the construction of the so called stochastic bisimulation function. Such function can be used to quantify the distance between a system and its approximate abstraction. The work in this paper generalizes our earlier work for jump linear stochastic systems (JLSS). In this paper we demonstrate that linear stochastic hybrid automata can be cast as a modified JLSS and modify the procedure for constructing the stochastic bisimulation function accordingly. The construction of quadratic stochastic bisimulation functions is essentially a linear matrix inequality problem. In this paper, we also discuss possible extensions of the framework to handle nonlinear dynamics and variable rate Poisson processes. As an example, we apply the framework to a chain-like stochastic hybrid automaton.