Finite-Time Annular Domain Stochastic Stability for Impulsive Stochastic Delay System

This paper exhibits the analysis of the finite-time annular domain stochastic stability for impulsive stochastic delay systems. This kind of stability in the mean square of the underlying systems presents that when the value of the initial condition belongs to a certain interval, during a predetermined time interval, the state estimation of the underlying systems not only does not exceed a given upper bound, but also does not fall below a given lower bound. By employing the Lyapunov function, the Halanay inequality of integral type, and the theory of stochastic analysis, the finite-time annular domain stochastic stability in the mean square is considered for stochastic delay systems with impulses and delay impulses, respectively. Sufficient conditions are obtained to guarantee the finite-time annular domain stochastic stability in the mean square. Two impulsive control algorithms are proved to finite-time annular domain stabilize the underlying systems. The feasibility of the results obtained is checked by three examples.