  Analysis and design of filtered-x adaptive algorithms are conventionally done
by assuming that the transfer function in the secondary path is a discrete-time
system. However, in real systems such as active noise control, the secondary
path is a continuous-time system. Therefore, such a system should be analyzed
and designed as a hybrid system including discrete- and continuous- time
systems and AD/DA devices. In this article, we propose a hybrid design taking
account of continuous-time behavior of the secondary path via lifting
(continuous-time polyphase decomposition) technique in sampled-data control
theory.
