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IEEE Conference on Decision and Control (CDC)

Tangential interpolatory projection for model reduction of completely passive linear quantum stochastic systems

Onvaree Techakesari, Hendra I. Nurdin

Published Dec 1, 2015• 0 citations
Publisher

Abstract

This paper presents a tangential interpolatory projection model reduction method for the class of completely passive linear quantum stochastic systems, often encountered in quantum optics and related fields. We show that the important physical realizability property of the full-order system is preserved through the interpolatory projection approximation. Sufficient conditions that guarantee asymptotic stability and minimality of the reduced-order approximation are established. We also present an optimization based routine for selection of interpolation points and propose a heuristic approach to select tangent directions, the key elements of the interpolatory projection method for multiple-input multiple-output systems. An example is presented to illustrate the utility of our proposed approach.

DOI
10.1109/cdc.2015.7403447

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This paper concerns the recently proposed quasi-balanced truncation model reduction method for linear quantum stochastic systems. It has previously been shown that the quasi-balanceable class of systems (i.e. systems that can be truncated via the quasi-balanced method) includes the class of completely passive systems. In this work, we refine the previously established characterization of quasi-balanceable systems and show that the class of quasi-balanceable systems is strictly larger than the class of completely passive systems. In particular, we derive a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability Gramian of such systems. Exploiting this result, we prove that all linear quantum stochastic systems with a pure Gaussian steady-state (active systems included) are all quasi-balanceable, and establish a new complete parameterization for this important class of systems. Examples are provided to illustrate our results.