Filtering for discrete-time Markov jump systems with network transmitted mode

This paper is concerned with H₂ and H_∞ filter design for discrete-time Markov jump systems. The usual assumption of mode-dependent design, where the current Markov mode is available to the filter at every instant of time is substituted by the case where that availability is subject to another Markov chain. In other words, the mode is transmitted to the filter through a network with given transmission failure probabilities. The problem is solved by modeling a system with N modes as another with 2N modes and cluster availability. We also treat the case where the transition probabilities are not exactly known and demonstrate our conditions for calculating an H_∞ norm bound are less conservative than the available results in the current literature. Numerical examples show the applicability of the proposed results.