Multirate digital control design of an optimal regulator via singular perturbation theory

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Abstract
In this paper a multirate digital control design of an optimal regulator is investigated via singular perturbation theory. It is shown that the singularity perturbed continuous-time regulator leads, under slow and fast sampling rates, to two different discrete-time versions. They are decomposed into slow and fast subsystems, and then these solutions are combined in a proper way. Within the framework of such a decomposition-coordination principle, a multirate control design is developed naturally. Furthermore, the problem of the asymptotic stability of a multirate controlled system is investigated and the relationship between the original continuous-time version and the multirate controlled version is discussed.