Stability of discrete-time linear systems with Markovian jumping parameters and constrained control

The note is devoted to the study of linear discrete-time systems with Markovian jumping parameters and constrained control. The constraints used in the note are of symmetrical inequality type. The approach of positively invariant sets is used to obtain new necessary and sufficient conditions for positive invariance, and sufficient conditions for stochastic stability. These conditions become those given for stationary discrete-time systems with one mode (deterministic linear discrete-time systems) as known in the literature