Almost sure stability criteria for linear Markovian switching systems

We present some stability criteria mainly for continuous-time Markovian switching systems, which can provide us with an insight into the mechanism that drives the subsystems to interact with each other so as to achieve stability. On the one hand, directly computing the Lyapunov exponent through the state-transition matrix of the system under consideration allows us to capture the interaction of subsystems by using the method developed in discrete-time setting. On the other hand, we can make sense of how the subsystems are orchestrated by the statistical property of switching signal through a family of coupled Lyapunov inequalities, which naturally covers the stability in the mean-square sense as a special case. Three examples are included to illustrate the theoretical results.