Optimal control of sampled data systems with state-and control-dependent noises

The paper is concerned with optimal control of linear stationary discrete time systems affected by an additive external noise and multiplicative noises. The intensities of one are linearly dependent on the vector of phase coordinates and on the control vector. The performance functional is a stationary mean of the sum of quadratic forms of the vectors of phase coordinates and control. Sufficient conditions and conditions for optimality of feasible control are obtained. Existence and uniqueness of a solution of a set of matrix equations is studied from which the matrix of optimal control coefficients is found. A way to choose weight matrices of the performance functional is proposed.