Joint Optimal Design of Digital Filters and State-Space Realizations

In this brief, a procedure for digital filters design is presented. The main purpose is to show that a digital filter and its realization can be simultaneously determined such as to minimize an upper bound of the H₂ norm of the estimation error and impose a certain degree of robustness against practical uncertainties as for instance, finite word length implementation, roundoff errors, and numerical precision. The optimal filter and its state-space realization are jointly determined from the solution of a convex programming problem expressed in terms of linear matrix inequalities. A simple illustrative example is presented for comparison purposes making clear the advantages of the reported results