Nonlinear feedback systems perturbed by noise: Steady-state probability distributions and optimal control

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.