THE H2 PROBLEM FOR SAMPLED-DATA SYSTEMS

In this paper we pose and give a complete solution to an analog of the H-2 problem for sampled-data system. We motivate and develop a natural generalization of the H-2 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 H-2 space of Hilbert-Schmidt operator valued functions. We give state space solutions to the optimal and suboptimal controllers synthesis problems in this new norm by establishing an equivalent standard H-2 problem.