Vladimirov, IgorPetersen, IanJames, MatthewFindeisen, RolfHirche, SandraJanschek, KlausMonnigmann, Martin2023-08-282023-08-28July 11-17http://hdl.handle.net/1885/296900This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a bounded time interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its infinite-horizon asymptotic growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formula expresses the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide an illustrative numerical example with a two-mode open quantum harmonic oscillator.This work is supported by the Air Force Office of Scientific Research (AFOSR) under agreement number FA2386-16-1-4065 and the Australian Research Council under grant DP180101805application/pdfen-AU© 2020 The Authors.https://creativecommons.org/licenses/by-nc-nd/4.0/Linear quantum stochastic systemsquadratic-exponential functionalsfrequency-domain representation202010.1016/j.ifacol.2020.12.1382022-07-24Creative Commons Attribution-NonCommercial-NoDerivs License