Stability of Stochastic Differential Delay Systems With Integral/Fragment‐Integral Term and Applications

ABSTRACT This article investigates the stochastic stability of stochastic differential delay systems (SDDSs) with path information and their applications in consensus control of multi‐agent systems (MASs) based on the path information feedback. Here, the integral path information and fragment‐integral path information are considered, respectively. The mean square (m.s.) and almost sure (a.s.) exponential stability criteria of the SDDSs with path integral information are established respectively according to the two types of path information. It is shown that the fragment‐integral term may work positively for stochastic stability. Moreover, the obtained stochastic stability theorems are applied to design a distributed proportional integral/fragment‐integral control protocol and establish consensus conditions for stochastic MASs under proportional‐integral (PI)‐type controls. Finally, the effectiveness of the results is verified through two simulation examples.