Stabilization of Discrete-time Linear Systems with Markov Switching in the Presence of Delays in Transmission of the Date

In this note we investigate the problem of the designing of a stabilizing static output feedback gain for a discrete time linear system affected by a Markov chain in the presence of a possible delay in the transmission of the measurements. We provide a set of conditions guaranteeing the existence of a such feedback gain. They are derived via some suitable criteria for exponential stability in mean square of discrete-time linear systems with coefficients depending upon the present state at time t and the state at time t - 1 of the Markov chain.