A Result on Almost Sure Stability of Linear Continuous-Time Markovian Switching Systems

This work investigates the almost sure stability for linear Markovian switching systems in continuous time by using Lyapunov function method. The distribution of switching points is combined into constructing the Lyapunov function, which gives rise to the fluctuation in bounding the transient phase over the time interval confined between two successive switching points due to the randomness of their locations. Showing that the influence of the accumulated fluctuations, by averaging it out, will be negligible, is the key step in proving our stability result. Illustrative examples are included to show the effectiveness of the theoretical result.