  This paper is concerned with infinite-horizon growth rates of
quadratic-exponential functionals (QEFs) for linear quantum stochastic systems
driven by multichannel bosonic fields. Such risk-sensitive performance criteria
impose an exponential penalty on the integral of a quadratic function of the
system variables, and their minimization improves robustness properties of the
system with respect to quantum statistical uncertainties and makes its
behaviour more conservative in terms of tail distributions. We use a
frequency-domain representation of the QEF growth rate for the invariant
Gaussian quantum state of the system with vacuum input fields in order to
compute it in state space. The QEF rate is related to a similar functional for
a classical stationary Gaussian random process generated by an infinite cascade
of linear systems. A truncation of this shaping filter allows the QEF rate to
be computed with any accuracy by solving a recurrent sequence of algebraic
Lyapunov equations together with an algebraic Riccati equation. The state-space
computation of the QEF rate and its comparison with the frequency-domain
results are demonstrated by a numerical example for an open quantum harmonic
oscillator.
