Stability and robust stability analysis for Markovian jump systems with state delay and more general transition probabilities

This paper considers the problem of delay-dependent stability and robust stability analysis for Markovian jump systems(MJSs) with state delay and more general transition probabilities. The time-delay is considered to be time-varying delays and has upper bounds. The transition probabilities of mode jumps include completely known, boundary known and completely unknown ones. In order to get less conservative criterion, the state information is used as much as possible to construct the Lyapunov-Krasovskii functional, and some new approaches are taken to deal with the partly known transition probabilities. Then, the sufficient conditions for stability and robust stability performance of the underlying systems are proposed. Finally, numerical examples are provided to demonstrate the effectiveness of the resulting criteria.