Robust ℋ∞ filtering for uncertain Markovian jump linear systems

This paper investigates the problem of ℋ_∞ filtering for a class of uncertain Markovian jump linear systems. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the system state-space model, including the coefficient matrices of the noise signals. It is also assumed that the jumping parameter is available. We develop a methodology for designing a Markovian jump linear filter that ensures a prescribed bound on the L₂-induced gain from the noise signals to the estimation error, irrespective of the uncertainty. The proposed design is given in terms of linear matrix inequalities