This paper deals with the problem of robust H∞ fault detection filter(FDF) design for a class of linear Markovian
jump systems with interval time-delay. By using an adaptive observer based FDF as a residual generator, the design of
robust H∞-FDF is formulated in the framework of stochastic ??∞ filtering. By applying Lyapunov-Krasovskii approach
and introducing some slack matrices, a delay-dependent sufficient condition on the existence of H∞-FDF is derived. The
parameter matrices to the H∞-FDF can be obtained by solving a set of linear matrix inequalities(LMI). A numerical example
shows the effectiveness of the proposed method.