Abstract
This paper considers the optimal design problem of a discrete-time time-invariant linear compensator for a linear control system with inaccessible states. It is assumed that the control system is also discrete-time and timeinvariant and that its initial states are unknown, but only their mean and covariance are known. The performance index for this problem is a quadratic cost averaged over initial state values.
To obtain the optimal compensator, this problem (Problem 1) is changed to two problems: problem 2 of designing an optimal compensator for a linear stochastic control system minimzing a performance index in steady-state, and Problem 3 of minimizing an average performance index per unit of time. Problem 3 is solved at first.
A separation theorem is shown. The optimal compensator is optimal in all linear control laws, and is constructed by using the optimal state-estimate observer and the feedback gain which is optimal in the complete state feedback.
