Lyapunov-Type Criteria of Absorbing Continuous-Time Markov Chains

The Lyapunov stability theory is developed for absorbing continuous-time Markov chains (CT-MCs) in this technical note. The derived stability criteria are all necessary and sufficient for absorbing CT-MCs and set absorbing CT-MCs, where Lyapunov functions can be constructed in a polynomial amount of time with respect to the cardinality of state spaces. Furthermore, the gap between Lyapunov functions of the CT-MCs and of the discrete-time Markov chains is bridged by the feature that the length of the sampling period in the sampled-data CT-MCs does not affect the reachability. The results presented here provide a novel insight for efficient analysis and synthesis of large-scale CT-MCs in the same manner as in dynamic systems. The applicability of these novel theoretical results is demonstrated via practical bioinspired networks from the literature.