  This paper is concerned with linear stochastic control systems in state
space. The integral of the squared norm of the system output over a bounded
time interval is interpreted as energy. The cumulants of the output energy in
the infinite-horizon limit are related to Schatten norms of the system in the
Hardy space of transfer functions and the risk-sensitive performance index. We
employ a novel performance criterion which seeks to minimize a combination of
the average value and the variance of the output energy of the system per unit
time. The resulting linear quadro-quartic Gaussian control problem involves the
H2 and H4-norms of the closed-loop system. We obtain equations for the optimal
controller and outline a homotopy method which reduces the solution of the
problem to the numerical integration of a differential equation initialized by
the standard linear quadratic Gaussian controller.
