D. Liberzon et Rw. Brockett, Nonlinear feedback systems perturbed by noise: Steady-state probability distributions and optimal control, IEEE AUTO C, 45(6), 2000, pp. 1116-1130
In this paper we describe a class of nonlinear feedback systems perturbed b
y white noise for which explicit formulas for steady-state probability dens
ities can be found, We show that this class includes what has been called m
onotemperaturic systems in earlier work and establish relationships with Ly
apunov functions for the corresponding deterministic systems. We also treat
a number of stochastic optimal control problems in the case of quantized f
eedback, with performance criteria formulated in terms of the steady-state
probability density.