H2H2 optimization and fixed poles of sampled-data systems under colored noise

The paper considers the sampled-data control problem for multivariable continuous LTI processes when colored stationary stochastic disturbances act on their inputs. The design problem is to find a causal stabilizing controller, which ensures the minimal value of the mean output variance. Based on the parametric transfer matrix (PTM) concept, a constructive polynomial solution of that design problem is provided. A number of general properties of the optimal system is derived, which are important for practical applications. In particular, the existence of fixed poles is shown. A consequence of this fact is a principal performance limitation of the H2H2 optimal control loop.