Compensatability and optimal compensation of systems with white parameters

The optimal compensation problem is considered in the case of linear discrete-time systems with stationary white parameters and quadratic criteria. A generalization of the notion of mean square stabilizability, namely mean square compensatability, is introduced. It is shown that suitable mean square compensatability and detectability conditions are sufficient, and necessary in general, for the existence of a unique optimal mean square stabilizing compensator. Tests are given to determine whether or not a system is mean square compensatable. It is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator. The results are illustrated with examples