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Approximations of Stochastic Hybrid Systems (2009)
| Citations: | 12 - 0 self |
BibTeX
@MISC{Julius09approximationsof,
author = {A. Agung Julius and George J. Pappas},
title = {Approximations of Stochastic Hybrid Systems},
year = {2009}
}
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Abstract
This paper develops a notion of approximation for a class of stochastic hybrid systems that includes, as special cases, both jump linear stochastic systems and linear stochastic hybrid automata. Our approximation framework is based on the recently developed notion of the so-called stochastic simulation functions. These Lyapunov-like functions can be used to rigorously quantify the distance or error between a system and its approximate abstraction. For the class of jump linear stochastic systems and linear stochastic hybrid automata, we show that the computation of stochastic simulation functions can be cast as a tractable linear matrix inequality problem. This enables us to compute the modeling error incurred by abstracting some of the continuous dynamics, or by neglecting the influence of stochastic noise, or even the influence of stochastic discrete jumps.
Keyphrases
stochastic hybrid system linear stochastic hybrid automaton jump linear stochastic system so-called stochastic simulation function stochastic discrete jump lyapunov-like function continuous dynamic index term approximation approximate abstraction developed notion stochastic noise approximation framework modeling error tractable linear matrix inequality problem special case stochastic simulation function
