On input-to-state stability for stochastic coupled control systems on networks

• We construct a model of stochastic coupled control systems on networks.
• We present sufficient conditions for two kinds of input-to-state stability.
• We mainly apply Lyapunov method and generalized Kirchhoff’s matrix tree theorem in graph theory.
• The stability criteria are presented in terms of the topology property of the network.

This paper investigates the input-to-state stability (ISS) properties for stochastic coupled control systems on networks (SCCSNs). With the help of Lyapunov method and graph theory, some inequality techniques and stochastic analysis skills, some sufficient criteria are obtained for eλt-weighted integral ISS in mean and almost sure exponential ISS of SCCSNs. These sufficient criteria are closely related to the topological property of the network anatomy. Finally, an example is given to illustrate the results.