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