Mean square exponential input-to-state stability of stochastic Markovian reaction-diffusion systems with impulsive perturbations

Abstract

Mean square exponential input-to-state stability (MSEISS) is considered for stochastic Markovian reaction-diffusion systems (SMRDSs) with impulsive perturbations. Both the boundary input and distributed input are considered in SMRDSs. With the Lyapunov–Krasovskii functional method, impulse theory and inequality techniques, a sufficient condition is established to achieve the MSEISS for SMRDSs with completely known transition rate matrix. Moreover, combined with the obtained sufficient conditions, the effects of the impulse and diffusion terms on MSEISS are demonstrated by examples. Then, the case is studied that the transition rate matrix is partially unknown and sufficient conditions are presented to ensure the MSEISS in light of the introduced free constants. Finally, two numerical examples are given to illustrate the validity of our theoretical results.