Optimal sampled-data approximation in the ν-gap metric

We revisit the problem of optimal sampled-data approximation with respect to a -gap measure of error. A method, exploiting standard computational tools for H sampled-data synthesis, is devised to solve weighted approximation problems of this kind. Our development relies on recently established shift-invariant representations for linear time-invariant systems and periodic sampled-data systems defined over the doubly-infinite time axis. It also involves a single J-spectral factorisation; by contrast, existing results involve a more complicated factorisation. To conclude, two numerical examples are considered.