H2 optimal linear robust sampled-data filtering design using polynomial approach

A new frequency domain approach to robust multi-input-multi-output (MIMO) linear filter design for sampled-data systems is presented. The system and noise models are assumed to be represented by polynomial forms that are not perfectly known except that they belong to a certain set. The optimal design guarantees that the error variance is kept below an upper bound that is minimized for all admissible uncertainties. The design problem is cast in the context of H₂ via the polynomial matrix representation of systems with norm bounded unstructured uncertainties. The sampled-data mix of continuous and discrete time systems is handled by means of a lifting technique; however, it does not increase the dimensionality or alter the computational cost of the solution. The setup adopted allows dealing with several filtering problems. A simple deconvolution example illustrates the procedure.