H ∞ filtering for discrete‐time Markov jump systems with unknown transition probabilities

Abstract

SUMMARYThis paper investigates the state estimation problem for a class of Markov jump systems with unknown transition probabilities (TPs). Considering more general cases where the TPs are unknown, but the distribution of TPs can be approximated by Gaussian process, we use the Gaussian transition PDF to describe the random distribution characteristics of TPs. With the proposed PDF description, the corresponding Markov jump systems can cover the systems with precisely known and partially known TPs as two special cases. A discretization method is firstly developed to obtain the expectation of TPs from the Gaussian PDF. Then, an H ∞ filter is designed such that the closed‐loop systems are stochastically stable and the estimation error satisfies a given noise attenuation level. Finally, a numerical example is worked out to illustrate the effectiveness of the theoretical results.Copyright © 2013 John Wiley & Sons, Ltd.