H2 filtering through multi-hop networks: Trade-off analysis between the network consumption and performance degradation

Consider the problem of H
₂
filtering of a linear system in a networked control system scenario. More precisely, the communication between the system and the filter is accomplished through a multi-hop network where packet loss, modeled by a Markov chain with a Bernoulli distribution, may occur. The purpose of this paper is to investigate the trade-off between the network resource saving and the performance degradation, analyzing in particular: i) the influence of the initial probability distribution on the design of the filter; ii) the relation of the mean square error of estimation with the probability of successful transmissions, the adopted transport scheme or the number of maximum allowable transmissions per data packet. Additionally, a comparison between H
₂
and H
_∞
filtering is also performed. The results are obtained for a particular case study based on a Furuta's inverted pendulum.