Towards less conservative stabilisation conditions for Markovian jump linear systems with partly unknown transition probabilities

The problem of deriving less conservative stability and stabilisation conditions for a class of discrete-time Markovian jump linear systems with partly unknown transition probabilities is investigated. To do so, traditional conditions under consideration are first formulated to be with homogeneous polynomial dependence on partly unknown transition probabilities, and then be converted into a finite set of linear matrix inequalities via a relaxation process that can incorporate all possible slack variables coupled with transition probabilities.