Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems

Abstract

This note addresses the problem of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filtering for continuous-time linear systems with Markovian jumping parameters. The main contribution of the note is to provide a method for designing an asymptotically stable linear time-invariant H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> 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