Robust Stability of Perturbed Continuous-Time Markov Chains

This paper studies the stability of perturbed continuous-time Markov chains (CT-MCs) by establishing stability criteria and robustness indicators. The robust stability criteria are derived from the spatial relationships between reachable sets and invariant subsets. Moreover, a robustness indicator is formulated to quantify the ability of each transition to resist perturbations affecting the stability, where lower values signify more critical transitions. Finally, a biological case study demonstrates the applicability of the theoretical result. This framework not only facilitates stability assessments for perturbed CT-MCs but also identifies critical transitions, the monitoring of which can enhance system resilience.