H∞ filtering for discrete-time piecewise homogeneous Markov jump Lur´e systems with application to economic systems

This paper addresses the robust H_∞ filtering problem for a class of Markov jump Lur´e systems with time-varying transition probabilities in discrete-time domain. The time-varying character of transition probabilities is considered to be finite piecewise homogeneous. A full-order filter is designed such that the resulting closed-loop systems are stochastically stable and have a guaranteed H_∞ performance index in terms of linear matrix inequalities. The effectiveness and potential of the developed results are verified through an example about a class of economic systems.