Variance-constrained H∞ state estimation for time-varying multi-rate systems with redundant channels: The finite-horizon case

This paper deals with the H∞ state estimation problem for a class of networked multi-rate time-varying systems with estimation error variance constraint. The redundant channel transmission scheme is employed to reduce the packet dropout rate and improve the quality of the data delivery. By utilizing the lifting technique, an augmented estimation error system is established with a uniform sampling rate. The objective of this paper is to design a time-varying state estimator such that, in the simultaneous presence of the asynchronous sampling, probabilistic packet dropouts as well as stochastic noises, the error dynamics of the state estimation satisfies both the prescribed H∞ performance requirement and the prescribed estimation error variance constraints. Through intensive stochastic analysis, sufficient conditions are established to ensure the existence of the desired estimator whose parameters are determined by solving a set of recursive linear matrix inequalities. A numerical example is presented to show the validity of the proposed estimation strategy.