H∞ filtering for networked systems with partly known distribution transmission delays

This paper studies the H∞ filtering problem for a class of discrete-time networked systems with partly known distribution transmission delays. It is assumed that the random sensor-filter delay satisfies Markovian characteristics, but the transition probabilities of the delay transferring from one value to others are partly known. A novel measurement model is proposed to reflect the random delay of the transmission modes and the resulting filtering error system is modeled as a Markovian jump system (MJS) with multiple modes and state delay. Sufficient conditions are derived for the filtering error system to be stochastically stable and ensure a prescribed H∞ disturbance attenuation level bound by using mode-dependent Lyapunov functional approach. Based on the derived conditions, a design procedure for the H∞ filter is also presented. A numerical example is provided to show the design process of the filter and the effectiveness of the proposed method.