Abstract
The solutions to the optimal l/sup 2/ to l/sup 2/ disturbance rejection problem (H/sup infinity /) as well as to the LQG (linear quadratic Gaussian) (H/sup 2/) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H/sup infinity / problem is solved using the Nehari's theorem, whereas in the H/sup 2/ problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H/sup infinity / and H/sup 2/ problems in periodic systems applies when considering the same problems in multirate sampled data systems. >
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