Sparse H2 optimal filter design via convex optimization

This paper considers the problem of synthesizing H₂ filters subject to sparsity constraints on their structure, that is, constraints on which inputs can be used when computing the estimated value of a given output. The main result of the paper shows that, contrary to the sparse controller case, the necessary and sufficient condition for the existence of filters satisfying a given sparsity pattern is related to the existence of solutions to a finite set of linear equations. Further, when the problem is feasible, then it can be solved using convex optimization and the objective function exhibits a “separation” like structure that clearly indicates the cost of sparsity.