I. Introduction
Sampled-data (SD) systems have attracted much attention from academia and industry, and a great number of results about SD systems have been reported so far, see for example, [1]–[3]. Multirate sampling is very common in sampled-data control systems, and widely used in flight control [4] and other cases where there is more than one sampling rate. Multirate sampled-data was first brought out by Kranc in 1957 with the use of switch decomposition to design a stabilization controller [5]. Kalmen [6] and Firedland [7] also did pioneering works of multirate sampled-data systems. A lifting technique was described by Meyer in 1990 to reduce the periodic system problem to a norm-equivalent discrete-time system problem [8], which can be studied by standard methods. Then this classic work has continued to attract researchers so far.