Robust dissipative filtering for discrete-time Markov jump Lur´e systems with uncertain transition probability matrix

This paper addresses the dissipative filtering problem for a class of Markov jump Lur´e systems with uncertain transition probabilities in discrete-time domain. The uncertain characteristic of the transition probability matrix is modelled in accordance with the Cartesian product of simplexes, called multi-simplex. A full-order filter is designed such that the resulting error systems are stochastically stable and strictly (Q, S, R)-γ-dissipative. Sufficient conditions for the existence of desired filter are derived in terms of linear matrix inequalities relaxations. As the main tool we employ a polynomially parameter-dependent Lyapunov function, which depends on the uncertain parameters and the sector condition assumption for the nonlinearities. A numerical example is presented to show the effectiveness of the developed theoretical results.