H ₂ filter design for discrete-time Markov jump linear systems with partly unknown transition probabilities

The H ₂ filter design problem for discrete-time Markov jump linear systems with partly unknown transition probabilities is addressed in this paper. The so-called partly unknown transition probabilities cover two cases: one is that some unknown elements have known lower and upper bounds, the other is that some unknown elements have no information available. By employing Finsler's lemma and linear matrix inequality (LMI) technique, sufficient conditions are developed in the LMI setting to design an H ₂ filter such that the filtering error system is mean-square stable and at the same time satisfies a prescribed H ₂ performance index. Numerical examples are presented to illustrate the effectiveness of the developed theoretical results.