Less conservative stabilization conditions for Markovian jump systems with partly unknown transition probabilities

This paper is devoted to the robust stabilization problem for a class of MJLSs with mode transition probabilities taken to be partly known, unknown, and unknown but with known bounds. To meet the needs of less conservative stabilization conditions, this paper proposes a valuable approach that (1) can express the conditions in terms of matrix inequalities with homogeneous polynomial dependence on partly unknown transition probabilities and (2) can include all possible slack variables related to transition probability constraints in the relaxation process coupled with deriving a finite set of linear matrix inequalities (LMIs). Finally, two numerical examples are reported to illustrate the effectiveness of the derived stabilization conditions.