Filtering of discrete‐time Markov jump linear systems with uncertain transition probabilities

This article addresses the filtering design problem for discrete‐time Markov jump linear systems (MJLS) under the assumption that the transition probabilities are not completely known. We present the methods to determine ℋ︁ 2 ‐ and ℋ︁ ∞ ‐norm bounded filters for MJLS whose transition probability matrices have uncertainties in a convex polytope and establish an equivalence with the ones with partly unknown elements. The proposed design, based on linear matrix inequalities, allows different assumptions on Markov mode availability to the filter and on system parameter uncertainties to be taken into account. Under mode‐dependent assumption and internal model knowledge, observer‐based filters can be obtained and it is shown theoretically that our method outperforms some available ones in the literature to date. Numerical examples illustrate this claim.