Sliding mode control for Markov jump linear uncertain systems with partly unknown transition rates

In this paper, based on sliding mode control approach, the robust stabilisation problem for a class of continuous-time Markovian jump linear uncertain systems with partly unknown transition rates is investigated. The transition rate matrix under consideration covers completely known, boundary known and completely unknown elements. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. Then a sliding mode control law is designed to drive the state trajectory of the closed-loop system to the specified linear switching surface in finite time in spite of the existing uncertainties and unknown transition rates. Finally, an example is given to verify the validity of the theoretical results.