On stability of time-inhomogeneous Markov jump linear systems

In this work we present necessary and sufficient conditions for mean square stability (MSS) of discrete-time time-inhomogeneous Markov jump linear systems (MJLS) affected by polytopic uncertainties on transition probabilities. We also prove that deciding MSS on such systems is NP-hard and that MSS is equivalent to exponential mean square stability (EMSS) and to stochastic stability (SS).