Departmental Papers (ESE)

Document Type

Journal Article

Date of this Version

5-27-2009

Comments

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Reprinted from:
Julius, A. A.; Pappas, G. J., "Approximations of Stochastic Hybrid Systems," Automatic Control, IEEE Transactions on , vol.54, no.6, pp.1193-1203, June 2009

URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4982634&isnumber=5071740

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.

Keywords

Approximation, bisimulation, stochastic hybrid systems, verification

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Date Posted: 06 July 2009

This document has been peer reviewed.