A refined stability result for linear Markovian switching systems and its implications

Abstract

We attempt to offer an informative insight into the stability mechanism of Markovian switching systems from the perspective of Lyapunov method. With this aim, our efforts are devoted to refining a stability criterion that was posed in Cong (2018) and moreover, showing that all kinds of existing results derived from Lyapunov method in principle can be recovered as special cases of the refined one, due to overlooking certain things that may influence stability. To do so, it requires us to fully understand the construction and the computation of the Lyapunov function used in proving our result, which in turn requires us to work with renewal theory other than confining ourselves within the context of Markov chain theory for describing switching signals.