Separation principle for multivariable control: a continuous-time polynomial systems approach

The separation principle for state-equation based stochastic optimal controllers is well known and provides engineering insights and a useful mechanism for implementation. A new equivalent result is established for output feedback, continuous-time systems represented in the frequency-domain by transfer-function or polynomial matrices. The LQG or H₂ optimal controller can be realised using an observer-based structure estimating pseudo-state variables that are fed back through a dynamic gain control block. There are normally fewer pseudo-states than the total order of the system. Unlike the state-space results, there are two separation principle results that are established, depending on the order in which the dual control and estimation problems are solved