Pointwise Stabilization of Discrete-time Stationary Matrix-valued   Markovian Chains
  We study the pointwise stabilizability of a discrete-time, time-homogeneous, and stationary Markovian jump linear system. By using measure theory, ergodic theory and a splitting theorem of state space we show in a relatively simple way that if the system is essentially product-bounded, then it is pointwise convergent if and only if it is pointwise exponentially convergent. 
Xiongping Dai, Yu Huang and Mingqing Xiao
math.PR cs.SY math.DS math.OC