Cost translation and a lifting approach to the multirate LQG problem

It is shown how to translate an instance of a multirate sampled-data LQG problem into an equivalent, modified, single-rate, shift-invariant problem via a lifting isomorphism approach. Using this approach, one can solve the multirate LQG problem without using periodic system theory or solving periodic Riccati equations and without suffering any increases in state dimension. This translation procedure shows the correct way to translate RMS noise specification to the lifted domain for a multirate Q-design computer-aided-design package.>