Distributed H<inf>∞</inf> consensus filtering of stochastic systems with markovian coupling intercommunication delays

This paper deals with the problem of distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus filtering for a continuous-time Itô-type stochastic system with Wiener process disturbances and Markovian coupling intercommunication delays. The problem is solved based on distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters in combination with consensus strategies. The set of filter nodes form a communication network whose topology is modeled by a directed graph that describes estimates exchanged among neighboring nodes. A refined technique is provided to tackle the complicated coupling of the exchanged estimates in the presence of random coupling intercommunication delays. Moreover, a sufficient condition on the existence of desired distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus-based filters is established such that the resultant filter error system is mean square exponentially stable with a weighting H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus performance index. The filter design problem is posed in terms of linear matrix inequalities. Finally an illustrative example is given to show the effectiveness of the proposed filter design method.