Stochastic LQ-optimal control for 2-D systems

Stochastic LQ-optimal control problem is solved for linear 2-D systems via 2-D polynomial techniques. All stabilizing controllers are parameterized and then minimizing one is obtained. Its transfer function results from two 2-D spectral factorizations and a couple of linear equations in formal power series. A practically useful sub-optimal controller is also considered that results from truncated spectral factorizations and a couple of 2-D polynomial equations.