Quantized state systems method: Difference between revisions

Revision as of 11:30, 6 July 2015

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==Theoretical properties==

In 2001, Ernesto Kofman proved<ref>{{cite journal | last=Kofman | first=Ernesto |title=A second-order approximation for DEVS simulation of continuous systems|year=2002 |journal = Simulation |volume=78 |pages=76&ndash;89 |url=http://sim.sagepub.com/content/78/2/76.short }}</ref> a remarkable property of the quantized-state system simulation method: namely, that when the technique is used to solve a [[Exponential stability|stable]] [[LTI system theory|linear time-invariant (LTI) system]], the global error is bounded by a constant that is proportional to the quantum, but (crucially) independent of the duration of the simulation. More specifically, for a [[Exponential stability|stable]] LTI system with the [[state-transition matrix]] <math>A</math>, for a multidimensional it was shown in [[Quantized state systems method|[CK06]]] that the absolute error vector <math>\vec{e}(t)</math> is bounded above by

:<math>\left| \vec{e}(t) \right| \leq \left| V \right|\ \left| \Re\left(\Lambda\right)^{-1} \Lambda \right|\ \left| V^{-1} \right|\ \Delta \vec{Q}</math>