Robust stochastic stability of discrete-time linear systems with Markovian jumping parameters

We study the problems of stability and stability robustness for a class of discrete-time linear systems with Markovian jumping parameters (DTLSMJP) with norm bounded uncertainties. A necessary and sufficient condition for stochastic stability is established using a Lyapunov exponent. The approach gives a direct expression of the second moment that allows us to conclude on the stochastic stability of the DTLSMJP in the mean-square sense. Under the assumption that the uncertainties are norm bounded a sufficient condition guaranteeing the robust stability of the uncertain discrete-time linear systems with Markovian jumping parameters (UDTLSMJP) is presented, and it is in terms of a set of coupled discrete-time algebraic Riccati equations