Robust $H_{\infty}$ filtering for networked systems with communication delay and data missing

In this paper, we deal with the
$H_{\infty}$
filtering problem for a class of discrete-time networked systems with communication delay and data missing. Two kinds of incomplete measurements with random delay and stochastic data missing are considered. The transition probabilities of the Markovian process are uncertain, but they exist in a convex set of known polyhedron types. The main purpose of this paper is to design a robust
$H_{\infty}$
filter, which makes the filtering error system stochastic stable and satisfies the given
$H_{\infty}$
performance index. A sufficient condition for the existence of the desired filter is established by using linear matrix inequalities. A numerical example shows the effectiveness and applicability of the method.