In serving the multirate sampled-data H-2 control problem using the lifting
approach, one needs to solve a constraint discrete-time H-2 optimal contro
l problem for a generalized plant with infinite dimensional input/output sp
aces. To solve this problem, the existing sampled-data H-2 design technique
computes an equivalent finite dimensional discrete-time system and then de
signs the optimal H-2 controller for the equivalent system. In this paper,
we will show that this problem can be solved using state space formulas by
dealing with operators directly. The operator compositions are computed exp
licitly using discrete multirate lifting and matrix exponentials. The advan
tages of the direct method are: it is straightforward, it has clear physica
l meanings, and it is more efficient computationally. A sufficient conditio
n for the existence and uniqueness of multirate sampled-data H-2 optimal co
ntroller is given in terms of the continuous-time plant. (C) 1998 Elsevier
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