Stochastic control of discrete systems: A separation principle for Wiener and polynomial systems

A new separation principle is established for systems represented in discrete frequency-domain Wiener or polynomial forms. The LQG or H-2 optimal controller can be realized using an observer based structure estimating noise free output variables that are fedback through a dynamic gain control block. The frequency-domain solution can be related to standard state-space Kalman filtering results, but it has a rather different structure. Surprising there are also two separation principle theorems depending upon the order in which the ideal output optimal control and the optimal observer problems are solved.