Sampling prefilters with an H∞ criterion

Sampling prefilters with an H_∞, performance criterion are studied. An important application area for sampling prefilters in H_∞, is the problem of designing optimal prefilters in the context of sampled-data H_∞, optimal control. The problem is to estimate a given linear function of the state of a continuous-time plant at discrete time instants. In this problem the process noise is a continuous L₂-signal, and the estimation error is a discrete signal in l₂. A continuous-time sampling prefilter is then designed so as to achieve an H_∞, performance bound. Conditions for the existence of a sampling prefilter that satisfies the performance bound are obtained, and explicit formulae for a filter which achieves the performance bound are given. It is also shown how the filters studied in this paper can be applied to the design of optimal prefilters in sampled-data H_∞, optimal control.