Stochastic integral input-to-state stability for stochastic delayed networked control systems and its applications

In this paper, stochastic integral input-to-state stability (SiISS) is studied for stochastic delayed networked control systems (SDNCSs). With the assistance of Lyapunov-Krasovskii functional, as well as stochastic analysis and inequality techniques, we establish a Lyapunov-type criterion that guarantees SiISS for SDNCSs. What is more, another sufficient criterion is proposed by means of coefficients in SDNCSs and it is proved to be very useful in practice. Based on the main theorems obtained, we investigate SiISS of two typical SDNCSs in details including stochastic coupled van der Pol oscillators on networks with time delay and stochastic Hopfield neural networks with time delay as applications. Last but not least, the effectiveness and applicability of our results are illustrated via corresponding numerical examples and simulation outcomes.