Control synthesis of Markovian jump fuzzy systems based on a relaxation scheme for incomplete transition probability descriptions

Abstract

The attention of this paper is focused on deriving less conservative stabilization conditions for Markovian jump fuzzy systems by introducing a relaxation scheme for incomplete transition probability descriptions. To this end, this paper proposes a representation approach that can express the considered conditions in terms of homogeneous polynomial of unknown and uncertain transition rates. Furthermore, based on this approach, this paper incorporates all possible slack variables into the relaxation process with consideration of the property of transition rates. Finally, three numerical examples are given to show the effectiveness of the derived stabilization conditions.