Filtering of discrete-time Markov jump linear systems with cluster observation: An approach to Gilbert-Elliot´s network channel

This paper addresses the ℋ_∞ and the ℋ₂ filtering design problems for linear systems whose outputs are transmitted through a Markovian channel. Previous works have used simplified Gilbert-Elliot network channel models to address burst errors in the output. We will use a generalized Gilbert-Elliot model, increasing the number of Markov modes. With this extended model it is not possible anymore to know exactly what the Markov mode at every instant of time is, but only that it belongs to a given subset we call cluster. The design of the filter is done using Linear Matrix Inequalities (LMIs).