New methods arc presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.