***ℋ∞ Filter Design through Multi-simplex Modeling for Discrete-time Markov Jump Linear Systems with Partly Unknown Transition Probability Matrix

Abstract

This paper addresses the problem of ***ℋ∞ filter design for discrete-time Markov jump linear systems (MJLS) with transition probability matrix affected by uncertainties. The proposed methodology allows to take into account the different types of uncertainties usually adopted in MJLS in a systematic way. New conditions are given for ***ℋ∞ filter design with partial, complete or null Markov mode availability. Due to the presence of slack variables in the synthesis conditions and to the use of homogeneous polynomial solutions of arbitrary degrees, less conservative linear matrix inequality relaxations can be obtained. Numerical experiments illustrate the better performance and efficiency of the proposed approach when compared to other strategies available in the literature.