In this paper, we examine the robust H-infinity filtering problem for a class of linear, uncertain discrete delay systems with Markovian jump parameters. The uncertainties are time-varying and norm-bounded parametric uncertainties and the delay factor is arbitrary constant. We provide initially a robust stochastic stability result with a prescribed performance measure. Then we design a linear causal filter using algebraic inequality procedure
which ensures a prescribed disturbance attenuation level from the disturbance signal to the filtering error.