Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control

•The criterion of finite-time stability is derived for SMRDSs based on a designed boundary controller.•The sufficient condition of SMRDSs is presented in case of the TRs being partially unknown.•For the SMRDSs, the fact that the case of completely known TRs is the special case of partially unknown TRs is discovered through our theoretical results. This paper investigates the finite-time stability (FTS) for a class of stochastic Markovian reaction-diffusion systems (SMRDSs). First, a boundary control strategy is put forward. Under the designed boundary controller, a sufficient condition of FTS for SMRDSs is provided based on the method of Lyapunov-Krasovskii functional combined with inequality techniques.When there exists the incompleteness of transition rate information, we further study the problem of SMRDSs with partially unknown transition rates (TRs) by adding a set of symmetric free matrices. An FTS criterion is also obtained for this case. Theoretical results show that the case of completely known TRs is the special case of partially unknown TRs. Finally, simulation examples are presented to verify the validity of our derived results.