Hybrid design of filtered-x adaptive algorithm via sampled-data control theory

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 analysed 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 behaviour of the secondary path via lifting (continuous-time polyphase decomposition) technique in sampled-data control theory.