On the quadratic sampled-data regulator with unstable random disturbances

This paper is concerned with the design of a digital controller, optimizing a quadratic cost function, for a linear system subjected to plant disturbance. The disturbance is viewed as a Gaussian random process generated by a linear system which may be unstable. It is shown that the optimal control consists of the sum of two terms: the optimal control when no disturbance is present and a term depending on the estimates of the disturbance. Necessary and sufficient conditions for the convergence of the gain matrices is given.