Finite-time H∞ filtering of Markov jump systems with incomplete transition probabilities: a probability approach

This paper concerns the finite-time H_∞ filtering of discrete Markov jump system with incomplete transition probabilities which cover the cases of known, uncertain and unknown. To include all possible cases, with the probability viewpoint, a truncated Gaussian distribution is employed to describe them. To ensure the filtering error systems to be finite-time stochastic stable with a prescribed noise attenuation level, sufficient conditions for the H_∞ filter design are yielded in terms of solvability of a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.