Direct digital design of general multirate sampled-data systems is considered. To tackle causality constraints, a new and natural framework is proposed using nest operators and nest algebras. Based on this framework explicit solutions to the H1 and H2 multirate control problems are developed in the frequency domain.

Direct digital design of general multirate sampled-data systems is considered. To tackle causality constraints, a new and natural framework is proposed using nest operators and nest algebras. Based on this framework explicit solutions to the H 1 and H 2 multirate control problems are developed in the frequency domain.

We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a quantitative measure of stable rank. These results are applied to compute the right (left) topological stable rank for all nest algebras. This value is either 2 or in...