Mode-independent H∞ filters for hybrid Markov linear systems

This paper addresses the problem of H_∞ filtering for continuous-time linear systems with Markovian jumping parameters. The main contribution of the paper is to provide a method for designing an asymptotically stable linear time-invariant H_∞ filter for systems where the jumping parameter is not accessible. The cases where the transition rate matrix of the Markov process is either exactly known, or unknown but belongs to a given polytope, are treated. The robust H_∞ filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a Lyapunov function that depends on the uncertain parameters is developed. The proposed filter designs are given in terms of linear matrix inequalities.