The H2 problem for sampled-data systems

The authors pose and give a complete solution to an analog of the H² problem for sampled-data systems. They develop a natural generalization of the H² cost to periodic systems, which is then applied to the continuous-time closed-loop mapping in a sampled-data control system. It is shown that the cost criterion developed is actually a norm in an H² space of Hilbert-Schmidt operator valued functions. State-space solutions are given to the optimal and suboptimal controllers synthesis problems in this new norm by establishing an equivalent standard H ² problem