Further criterion for stochastic stability analysis of semi‐Markovian jump linear systems

Summary This article is devoted to provide further criterion for stochastic stability analysis of semi‐Markovian jump linear systems (S‐MJLSs), in which more generic transition rates (TRs) will be studied. As is known, the time‐varying TR is one of the key issues to be considered in the analysis of S‐MJLS. Therefore, this article is to investigate general cases for the TRs that covered almost all types, especially for the type that the jumping information from one mode to another is fully unknown, which is merely investigated before. By virtue of stochastic functional theory, sufficient conditions are developed to check stochastic stability of the underlying systems via linear matrix inequalities formulation combined with a maximum optimization algorithm. Finally, a numerical example is given to verify the validity and effectiveness of the obtained results.