An LMI solution to the robust synthesis problem for multi-rate sampled-data systems

In this paper we address the asynchronous multi-rate sampled-data H-infinit y synthesis problem. Necessary and sufficient conditions are given for the existence of a controller achieving the desired performance, and the proble m is shown to be equivalent to a convex optimization problem expressed in t he form of linear operator inequalities. In the case where the sample and h old rates are synchronous, these operator inequalities reduce to linear mat rix inequalities, for which standard numerical software is available. (C) 2 001 Elsevier Science Ltd. All rights reserved.