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This study considers asymptotic stability in the mean square sense for stochastic delay Markovian reaction‐diffusion systems (SDMRDSs) via boundary control. Firstly, the authors present a boundary controller for the system. By constructing of a Lyapunov–Krasovskii functional and utilising of Poincaré inequality, a sufficient criterion of mean square asymptotic stability for SDMRDSs is established. Next, boundary control for stochastic Markovian reaction‐diffusion systems (SMRDSs) with time‐varying delays is also investigated, and a delay‐dependent sufficient condition for SMRDSs under the boundary control law is obtained. In addition, the robust boundary stabilisation of SMRDSs with parametric uncertainty is considered. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study addresses the problem of exponential stability for a class of impulsive positive systems with mixed time‐varying delays. A delayed impulsive positive system model is introduced for the first time and a necessary and sufficient condition guaranteeing the positivity of this kind of system is proposed. By using a copositive Lyapunov–Krasovskii functional and the average impulsive interval method, a sufficient criterion of global exponential stability for delayed impulsive positive systems is established in terms of linear programming problems. A numerical example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]