Linear discrete stochastic control with a reduced-order dynamic compensator

In continuous-time linear stochastic control with a fixed structure, reduced-order, dynamic compensator one obtains a quasisingular problem whereby part of the structure is arbitrary. The dual of this problem in discrete time is considered with a more general formulation. Using a quadratic performance index, the Hamiltonian for obtaining the necessary conditions is obtained which may be used to define the optimal linear reduced-order dynamic compensator and the controller gain. It is shown that the discrete problem does not have the quasisingular property of the continuous-time case as is seen by consideration of the Hamiltonian.