A linear-quadratic-Gaussian control problem with innovations-feedthrough solution

The structure of the separation-theorem solution to the standard linear-quadratic-Gaussian (LQG) control problem does not involve direct output feedback as a consequence of the form of the performance index. It is shown here that the performance index may be generalized in a natural fashion so that the optimal control law involves output feedback [or equivalently, innovations feedthrough (IF)]. Applications where this formulation may be advantageous are indicated through an examination of properties of the IF control law.