Sampled-Data H2 Smoothing with Generalized Sampling

This paper studies the sampled-data H2 smoothing problem in which a given A/D device (sampler) is allowed to be a generalized sampler and a D/A device (hold) is designed. This is a nontrivial extension of available results, where only the ideal sampler case was considered. Both infinite (fixed-interval smoothing) and finite (fixed-lag smoothing) preview cases are solved. The optimal estimators have the structure of the cascade of a discrete linear time-invariant smoother and a generalized hold, similarly to the ideal sampler case available in the literature. A remarkable difference from the filtering (no preview) case is that the optimal generalized hold does depend on the sampler.