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.

This paper addresses constrained attitude control problems of flexible spacecraft on SO(3) subject to external disturbances and stochastic uncertainties without modal variable measurement. To handle the attitude constraints, an artificial potential function (APF) is constructed based on the rotation matrix. By combining the super-twisting control technique and the APF, a robust control law is proposed to achieve constrained attitude control of flexible spacecraft with external disturbances. Furthermore, an adaptive robust control law is developed without prior information on the bound of the norm of flexible vibration and external disturbances. The results are then extended to the case that stochastic uncertainties exist and the adaptive robust control law is modified by designing a Lyapunov-function-based control parameter. Numerical simulations are presented to demonstrate the effectiveness of the proposed control laws.