On quantized H∞ filtering for multi-rate systems under stochastic communication protocols: The finite-horizon case

In this paper, the finite-horizon H∞ filtering problem is investigated for a class of linear discrete-time multi-rate systems with quantization effects under the stochastic communication protocol (SCP). The SCP is adopted to mitigate the undesirable data collision phenomenon resulting from the limited bandwidth of communication networks. Governed by a Markov chain, the SCP is employed to determine which sensor node should be granted the access right at each transmission instant. In order to cope with the difficulty caused by the asynchronous sampling, a lifting technique is utilized to convert the multi-rate system into a single-rate one with the identical slow sampling rate. The main purpose of the addressed problem is to design a set of time-varying filters for the multi-rate systems such that, for all admissible multi-sampling periods and quantization effects under the SCP, the H∞ constraint is satisfied over a finite-horizon. By resorting to the complete square method and the Riccati difference equation (RDE) technique, sufficient conditions are established to ensure the existence of the desired filters. Then, the filter parameters are explicitly expressed in terms of the solution to two coupled backward RDEs. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed filter design algorithm.