Encoding–Decoding‐Based Set‐Membership Filtering for Multirate Systems With Censored Measurement

ABSTRACT

This paper investigates the issue of set‐membership filtering (SMF) for time‐varying multirate systems with censored measurements. To meet practical transmission requirements, a multirate strategy is proposed to regulate the sampling rates of controlled devices and sensors. Furthermore, an encoding–decoding mechanism (EDM) is introduced to address the potential constraints on communication bandwidth and energy resources in industrial systems. By using the lifting technique, a filtering error is established based on a uniform sampling rate. With recursive linear matrix inequalities (RLMI), a sufficient condition for the realizability of the SMF is derived under the multirate mechanism, bounded noises, censored measurements as well as EDMs. Such a condition determines an ellipsoidal region that contains all possible real states at each time step. In addition, an optimization model utilizing the matrix trace as the metric is formulated under the corresponding inequality constraints, thereby yielding the ellipsoidal region of minimal volume. Finally, numerical simulations are used to verify that our designed filter is effective.